├── .gitignore ├── .idea └── dictionaries │ └── leland.xml ├── LICENSE ├── README.md ├── hypergraph ├── __init__.py ├── hypergraph.py └── pomset.py ├── notebook ├── enron analysis.ipynb └── enronNumericHypergraphEdgelist.txt └── setup.py /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | 5 | # C extensions 6 | *.so 7 | 8 | # Distribution / packaging 9 | .Python 10 | env/ 11 | build/ 12 | develop-eggs/ 13 | dist/ 14 | downloads/ 15 | eggs/ 16 | .eggs/ 17 | lib/ 18 | lib64/ 19 | parts/ 20 | sdist/ 21 | var/ 22 | *.egg-info/ 23 | .installed.cfg 24 | *.egg 25 | 26 | # PyInstaller 27 | # Usually these files are written by a python script from a template 28 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 29 | *.manifest 30 | *.spec 31 | 32 | # Installer logs 33 | pip-log.txt 34 | pip-delete-this-directory.txt 35 | 36 | # Unit test / coverage reports 37 | htmlcov/ 38 | .tox/ 39 | .coverage 40 | .coverage.* 41 | .cache 42 | nosetests.xml 43 | coverage.xml 44 | *,cover 45 | 46 | # Translations 47 | *.mo 48 | *.pot 49 | 50 | # Django stuff: 51 | *.log 52 | 53 | # Sphinx documentation 54 | docs/_build/ 55 | 56 | # PyBuilder 57 | target/ 58 | 59 | # Backup files 60 | *~ 61 | -------------------------------------------------------------------------------- /.idea/dictionaries/leland.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | cliquified 5 | directedness 6 | hyperedge 7 | hyperedges 8 | hypergraph 9 | ndarray 10 | pomset 11 | 12 | 13 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU LESSER GENERAL PUBLIC LICENSE 2 | 3 | Version 2.1, February 1999 4 | 5 | Copyright (C) 1991, 1999 Free Software Foundation, Inc. 6 | 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 7 | Everyone is permitted to copy and distribute verbatim copies 8 | of this license document, but changing it is not allowed. 9 | 10 | [This is the first released version of the Lesser GPL. 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IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE LIBRARY AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE LIBRARY (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE LIBRARY TO OPERATE WITH ANY OTHER SOFTWARE), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. 139 | 140 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Hypergraph 2 | 3 | A library for hypergraphs and hypergraph algorithms. Current focus is directed hypergraphs. 4 | 5 | Currently in early development, more to come soon... 6 | -------------------------------------------------------------------------------- /hypergraph/__init__.py: -------------------------------------------------------------------------------- 1 | from .pomset import POMSet 2 | from .hypergraph import Hypergraph 3 | -------------------------------------------------------------------------------- /hypergraph/hypergraph.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """ 3 | hypergraph.hypergraph: Basic hypergraph class. 4 | """ 5 | # Author: Leland McInnes 6 | # 7 | # License: LGPL v2 8 | 9 | import networkx as nx 10 | import itertools as itr 11 | import numpy as np 12 | 13 | from warnings import warn 14 | 15 | from collections import Counter, defaultdict 16 | from .pomset import POMSet 17 | 18 | 19 | class Hypergraph(object): 20 | """ 21 | A directed hypergraph consisting of nodes as edges. Each node or edge 22 | is an arbitrary python object, and associated to each node or edge, 23 | via the `node` and `edge` dictionaries, is a `POMSet` which provides 24 | a partially ordered multiset of either the nodes contained in an edge, 25 | or the edges incident upon a node. 26 | 27 | Parameters 28 | ---------- 29 | 30 | nodes : iterable, optional 31 | An iterable of nodes to initialize the hypergraph with, or None. 32 | (default None) 33 | 34 | default_node_order : string, optional 35 | A string (either 'none', default or 'total') specifying the ordering 36 | of the POMSets within the hypergraph 37 | 38 | Attributes 39 | ---------- 40 | 41 | node : dict 42 | A dictionary mapping each node object to its associated POMSet. 43 | 44 | edge : dict 45 | A dictionary mapping each edge object to its associated POMSet. 46 | 47 | nodes : iterable 48 | An iterable of all the node objects in the hypergraph. 49 | 50 | edges : iterable 51 | An iterable of all the edge objects in the hypergraph. 52 | """ 53 | 54 | node = {} 55 | edge = {} 56 | relation = {} 57 | 58 | def __init__(self, nodes=None, default_node_order='none'): 59 | if default_node_order not in ('none', 'total'): 60 | raise ValueError('Default node order must be one of: none, total') 61 | self.default_node_order = default_node_order 62 | if nodes is not None: 63 | for node in nodes: 64 | self.node[node] = POMSet([]) 65 | self.relation[self.node[node]] = node 66 | 67 | def node_objects(self): 68 | """Return a list (or iterable in python3) of the node 69 | objects of the hypergraph. 70 | """ 71 | return self.node.keys() 72 | 73 | def edge_objects(self): 74 | """Return a list (or iterable in python3) of the edge 75 | objects of the hypergraph. 76 | """ 77 | return self.edge.keys() 78 | 79 | def node_relations(self): 80 | """Return a list (or iterable in python3) of the node 81 | objects of the hypergraph. 82 | """ 83 | return self.node.values() 84 | 85 | def edge_relations(self): 86 | """Return a list (or iterable in python3) of the edge 87 | objects of the hypergraph. 88 | """ 89 | return self.edge.values() 90 | 91 | def neighbors(self, node): 92 | """Get a set of neighboring nodes. 93 | 94 | Parameters 95 | ---------- 96 | 97 | node : object 98 | The node to find the neighbors of. 99 | 100 | Returns 101 | ------- 102 | 103 | neighbors : set 104 | A set of all nodes neighboring the queries node. 105 | """ 106 | result = set([]) 107 | for edge in self.node[node]: 108 | result.update(self.edge[edge].labels) 109 | return result 110 | 111 | def weak_predecessors(self, node): 112 | """GGet a set of neighboring nodes weakly below the current node 113 | in any incident edges. 114 | 115 | Parameters 116 | ---------- 117 | 118 | node : object 119 | The node to find the neighbors of. 120 | 121 | Returns 122 | ------- 123 | 124 | neighbors : set 125 | A set of all nodes that are weak predecessors of the queries node. 126 | """ 127 | result = set([]) 128 | for edge in self.node[node]: 129 | for node_index in range(self.edge[edge].multiplcity()): 130 | result.update(self.edge[edge].weakly_below(node, node_index)) 131 | return result 132 | 133 | def weak_successors(self, node): 134 | """Get a set of neighboring nodes weakly above the current node 135 | in any incident edges. 136 | 137 | Parameters 138 | ---------- 139 | 140 | node : object 141 | The node to find the neighbors of. 142 | 143 | Returns 144 | ------- 145 | 146 | neighbors : set 147 | A set of all nodes that are weak successors of the queries node. 148 | """ 149 | result = set([]) 150 | for edge in self.node[node]: 151 | for node_index in range(self.edge[edge].multiplcity()): 152 | result.update(self.edge[edge].weakly_above(node, node_index)) 153 | return result 154 | 155 | 156 | def strict_predecessors(self, node): 157 | """Get a set of neighboring nodes strictly below the current node 158 | in any incident edges. 159 | 160 | Parameters 161 | ---------- 162 | 163 | node : object 164 | The node to find the neighbors of. 165 | 166 | Returns 167 | ------- 168 | 169 | neighbors : set 170 | A set of all nodes that are predecessors to the queries node. 171 | """ 172 | result = set([]) 173 | for edge in self.node[node]: 174 | for node_index in range(self.edge[edge].multiplcity()): 175 | result.update(self.edge[edge].strictly_below(node, node_index)) 176 | return result 177 | 178 | 179 | def strict_successors(self, node): 180 | """Get a set of neighboring nodes strictly above the current node 181 | in any incident edges. 182 | 183 | Parameters 184 | ---------- 185 | 186 | node : object 187 | The node to find the neighbors of. 188 | 189 | Returns 190 | ------- 191 | 192 | neighbors : set 193 | A set of all nodes that are successors to the queries node. 194 | """ 195 | result = set([]) 196 | for edge in self.node[node]: 197 | for node_index in range(self.edge[edge].multiplcity()): 198 | result.update(self.edge[edge].strictly_above(node, node_index)) 199 | return result 200 | 201 | 202 | def add_node(self, new_node): 203 | """Add a new node to the hypergraph. 204 | 205 | Parameters 206 | ---------- 207 | 208 | new_node : object 209 | The new node to add to the hypergraph 210 | """ 211 | self.node[new_node] = POMSet([]) 212 | self.relation[self.node[new_node]] = new_node 213 | 214 | def add_edge(self, new_edge, edge_labels, edge_order=None): 215 | """Add a new edge to the hypergraph. 216 | 217 | Parameters 218 | ---------- 219 | new_edge : object 220 | The edge object to add to the hypergraph. 221 | 222 | edge_labels : iterable 223 | An iterable of node objects that the edge relates. 224 | If the objects are not already nodes of the hypergraph 225 | then new nodes will be added to the hypergraph for them. 226 | 227 | edge_order : numpy ndarray (len(edge_labels), len(edge_labels)), optional 228 | The POMSET order of the edge, or None. If None the 229 | edge will be undirected (but can have dependencies added). 230 | (default None) 231 | """ 232 | self.edge[new_edge] = POMSet(edge_labels, edge_order) 233 | self.relation[self.edge[new_edge]] = new_edge 234 | 235 | for node in edge_labels: 236 | if node not in self.node: 237 | self.add_node(node) 238 | self.node[node].add_label(new_edge) 239 | if self.default_node_order == 'total': 240 | last_label = self.node[node].labels[-2] 241 | last_label_multiplicity = self.node[node].multiplicity(last_label) 242 | new_edge_multiplicity = self.node[node].multiplicity(new_edge) 243 | self.node[node].add_dependency(last_label, new_edge, 244 | from_index=last_label_multiplicity - 1, 245 | to_index = new_edge_multiplicity - 1) 246 | 247 | 248 | def add_bipartition_edge(self, new_edge, label_bipartition): 249 | """Add a new edge where the order is a bipartition into 250 | lower and upper elements. 251 | 252 | Parameters 253 | ---------- 254 | new_edge : object 255 | The edge object to add to the hypergraph. 256 | 257 | label_bipartition : list or tuple of iterables 258 | A list or tuple with two elements. The first is an iterable 259 | of all the lower labels. The second is an iterable of all the 260 | upper labels. 261 | """ 262 | self.edge[new_edge] = POMSet(bipartition=label_bipartition) 263 | self.relation[self.edge[new_edge]] = new_edge 264 | 265 | for node in label_bipartition[0]: 266 | if node not in self.nodes: 267 | self.add_node(node) 268 | self.node[node].add_label(new_edge) 269 | 270 | if self.default_node_order == 'total': 271 | last_label = self.node[node].labels[-2] 272 | last_label_multiplicity = self.node[node].multiplicity(last_label) 273 | new_edge_multiplicity = self.node[node].multiplicity(new_edge) 274 | self.node[node].add_dependency(last_label, new_edge, 275 | from_index=last_label_multiplicity - 1, 276 | to_index = new_edge_multiplicity - 1) 277 | 278 | 279 | for node in label_bipartition[1]: 280 | if node not in self.nodes: 281 | self.add_node(node) 282 | self.node[node].add_label(new_edge) 283 | 284 | if self.default_node_order == 'total': 285 | last_label = self.node[node].labels[-2] 286 | last_label_multiplicity = self.node[node].multiplicity(last_label) 287 | new_edge_multiplicity = self.node[node].multiplicity(new_edge) 288 | self.node[node].add_dependency(last_label, new_edge, 289 | from_index=last_label_multiplicity - 1, 290 | to_index = new_edge_multiplicity - 1) 291 | 292 | 293 | 294 | @property 295 | def dual(self): 296 | """Return a new hypergraph that is the dual of the current 297 | hypergraph. 298 | 299 | Returns 300 | ------- 301 | 302 | dual : Hypergraph 303 | The dual of the hypergraph. 304 | """ 305 | result = Hypergraph() 306 | result.node = self.edge.copy() 307 | result.edge = self.node.copy() 308 | return result 309 | 310 | @property 311 | def networkx_bipartite_representation(self): 312 | """Return a NetworkX graph of the bipartite representation of the 313 | hypergraph. 314 | 315 | Returns 316 | ------- 317 | 318 | graph : NetworkX Graph 319 | The bipartite representation graph. 320 | """ 321 | result = nx.Graph() 322 | result.add_nodes_from(self.nodes + self.edges) 323 | for edge in self.edges: 324 | for label in self.edge[edge].labels: 325 | result.add_edge(edge, label) 326 | 327 | return result 328 | 329 | @property 330 | def networkx_undirected_cliquification(self): 331 | """Return a NetworkX graph derived from the hypergraph by 332 | converting all hyperedges into graph cliques. 333 | 334 | Returns 335 | ------- 336 | 337 | graph : NetworkX Graph 338 | The cliquified graph. 339 | """ 340 | result = nx.Graph() 341 | result.add_nodes_from(self.nodes) 342 | for edge in self.edge: 343 | for n1, n2 in itr.combinations(self.edge[edge].labels, 2): 344 | result.add_edge(n1, n2) 345 | 346 | return result 347 | 348 | @property 349 | def networkx_weakly_directed_cliquification(self): 350 | """Return a NetworkX graph derived from the hypergraph by 351 | converting hypergraph edges into graph cliques weakly respecting 352 | directedness of hyperedges. 353 | 354 | That is, we create a graph edge between node `i` and node `j` if 355 | there exists a hyperedge that includes nodes `i` and `j` such 356 | that `j` is greater than or unrelated to `i` in that edge. 357 | 358 | Returns 359 | ------- 360 | 361 | graph : NetworkX Graph 362 | The cliquified graph. 363 | """ 364 | result = nx.Graph() 365 | result.add_nodes_from(self.nodes) 366 | for edge in self.edge: 367 | for n1 in self.edge[edge].support: 368 | for n1_index in range(self.edge[edge].multiplicity(n1)): 369 | for n2 in self.edge[edge].weakly_above(n1, n1_index): 370 | result.add_edge(n1, n2) 371 | 372 | return result 373 | 374 | @property 375 | def networkx_strictly_directed_cliquification(self): 376 | """Return a NetworkX graph derived from the hypergraph by 377 | converting hypergraph edges into graph cliques strictly respecting 378 | directedness of hyperedges. 379 | 380 | That is, we create a graph edge between node `i` and node `j` if 381 | there exists a hyperedge that includes nodes `i` and `j` such 382 | that `j` is strictly greater than `i` in that edge. 383 | 384 | Returns 385 | ------- 386 | 387 | graph : NetworkX Graph 388 | The cliquified graph. 389 | """ 390 | result = nx.Graph() 391 | result.add_nodes_from(self.nodes) 392 | for edge in self.edge: 393 | for n1 in self.edge[edge].support: 394 | for n1_index in range(self.edge[edge].multiplicity(n1)): 395 | for n2 in self.edge[edge].strictly_above(n1, n1_index): 396 | result.add_edge(n1, n2) 397 | 398 | return result 399 | 400 | def _bfs_recursion(self, search_root_list, directed='undirected'): 401 | next_layer = [] 402 | for node in search_root_list: 403 | for e in self.node[node]: 404 | if directed == 'undirected': 405 | next_layer.extend(self.edge[e].labels) 406 | elif directed == 'weakly': 407 | next_layer.extend(self.edge[e].weakly_above(node)) 408 | elif directed == 'strictly': 409 | next_layer.extend(self.edge[e].strictly_above(node)) 410 | else: 411 | ValueError('Directedness must be one of "undirected", weakly", "strictly"') 412 | 413 | if len(next_layer) > 0: 414 | result = [next_layer, [self._bfs_recursion(next_layer, directed=directed)]] 415 | else: 416 | result = [next_layer] 417 | 418 | return result 419 | 420 | def breadth_first_search(self, root, directed='undirected'): 421 | """Return a nested list representing the breadth first search of the 422 | hypergraph beginning at node `root`. 423 | """ 424 | result = [[root], self._bfs_recursion([root], directed=directed)] 425 | return result 426 | 427 | @property 428 | def undirected_size_distribution_matrix(self): 429 | """Return a matrix of size distributions (per node) where the 430 | (i, j)th entry is number of nodes with i edges of size j 431 | incident on the node. 432 | 433 | Returns 434 | ------- 435 | 436 | dist_matrix : numpy ndarray 437 | The size distribution matrix 438 | """ 439 | result_dict = defaultdict(int) 440 | for node in self.nodes: 441 | sizes = Counter(self.edge[e].size for e in self.node[node].labels) 442 | for i in sizes: 443 | j = sizes[i] 444 | result_dict[(i, j)] += 1 445 | 446 | matrix_dimensions = np.array(result_dict.keys()).max(axis=0) 447 | result = np.zeros(matrix_dimensions, dtype=int) 448 | for (i, j), count in result_dict.items(): 449 | result[i, j] = count 450 | 451 | return result 452 | 453 | @property 454 | def weakly_directed_out_size_distribution(self): 455 | """Return a matrix of size distributions (per node) where 456 | the (i, j)th entry is the number of nodes with i edges of 457 | out size (number of elements weakly above) j incident on 458 | the node. 459 | 460 | Returns 461 | ------- 462 | 463 | dist_matrix : numpy ndarray 464 | The size distribution matrix 465 | """ 466 | result_dict = defaultdict(int) 467 | for node in self.nodes: 468 | for e in self.node[node]: 469 | for node_index in range(self.edge[e].multiplicity(node)): 470 | sizes = Counter(len(self.edge[e].weakly_above(node, node_index))) 471 | for i in sizes: 472 | j = sizes[i] 473 | result_dict[(i, j)] += 1 474 | 475 | matrix_dimensions = np.array(result_dict.keys()).max(axis=0) 476 | result = np.zeros(matrix_dimensions, dtype=int) 477 | for (i, j), count in result_dict.items(): 478 | result[i, j] = count 479 | 480 | return result 481 | 482 | @property 483 | def weakly_directed_in_size_distribution(self): 484 | """Return a matrix of size distributions (per node) where 485 | the (i, j)th entry is the number of nodes with i edges of 486 | out size (number of elements weakly below) j incident on 487 | the node. 488 | 489 | Returns 490 | ------- 491 | 492 | dist_matrix : numpy ndarray 493 | The size distribution matrix 494 | """ 495 | result_dict = defaultdict(int) 496 | for node in self.nodes: 497 | for e in self.node[node]: 498 | for node_index in range(self.edge[e].multiplicity(node)): 499 | sizes = Counter(len(self.edge[e].weakly_below(node, node_index))) 500 | for i in sizes: 501 | j = sizes[i] 502 | result_dict[(i, j)] += 1 503 | 504 | matrix_dimensions = np.array(result_dict.keys()).max(axis=0) 505 | result = np.zeros(matrix_dimensions, dtype=int) 506 | for (i, j), count in result_dict.items(): 507 | result[i, j] = count 508 | 509 | return result 510 | 511 | @property 512 | def strictly_directed_out_size_distribution(self): 513 | """Return a matrix of size distributions (per node) where 514 | the (i, j)th entry is the number of nodes with i edges of 515 | out size (number of elements strictly above) j incident on 516 | the node. 517 | 518 | Returns 519 | ------- 520 | 521 | dist_matrix : numpy ndarray 522 | The size distribution matrix 523 | """ 524 | result_dict = defaultdict(int) 525 | for node in self.nodes: 526 | for e in self.node[node]: 527 | for node_index in range(self.edge[e].multiplicity(node)): 528 | sizes = Counter(len(self.edge[e].strictly_above(node, node_index))) 529 | for i in sizes: 530 | j = sizes[i] 531 | result_dict[(i, j)] += 1 532 | 533 | matrix_dimensions = np.array(result_dict.keys()).max(axis=0) 534 | result = np.zeros(matrix_dimensions, dtype=int) 535 | for (i, j), count in result_dict.items(): 536 | result[i, j] = count 537 | 538 | return result 539 | 540 | @property 541 | def strictly_directed_in_size_distribution(self): 542 | """Return a matrix of size distributions (per node) where 543 | the (i, j)th entry is the number of nodes with i edges of 544 | out size (number of elements strictly below) j incident on 545 | the node. 546 | 547 | Returns 548 | ------- 549 | 550 | dist_matrix : numpy ndarray 551 | The size distribution matrix 552 | """ 553 | result_dict = defaultdict(int) 554 | for node in self.nodes: 555 | for e in self.node[node]: 556 | for node_index in range(self.edge[e].multiplicity(node)): 557 | sizes = Counter(len(self.edge[e].strictly_below(node, node_index))) 558 | for i in sizes: 559 | j = sizes[i] 560 | result_dict[(i, j)] += 1 561 | 562 | matrix_dimensions = np.array(result_dict.keys()).max(axis=0) 563 | result = np.zeros(matrix_dimensions, dtype=int) 564 | for (i, j), count in result_dict.items(): 565 | result[i, j] = count 566 | 567 | return result 568 | 569 | @property 570 | def networkx_flag_digraph(self): 571 | warn('Not implemented yet!') 572 | return None 573 | -------------------------------------------------------------------------------- /hypergraph/pomset.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | """ 3 | hypergraph.pomset: Partially Ordered Multisets for use in directed 4 | hyperedges (and directed hypernodes). 5 | """ 6 | # Author: Leland McInnes 7 | # 8 | # License: LGPL v2 9 | import numpy as np 10 | 11 | def _is_bipartitite_order(order): 12 | for row in order: 13 | if np.any(row == -1) and any(row == 1): 14 | return False 15 | elif np.all(row == 0): 16 | return False 17 | 18 | return True 19 | 20 | def _get_bipartition(order): 21 | result = [[],[]] 22 | for index, row in enumerate(order): 23 | if np.any(row == -1): 24 | result[0].append(index) 25 | elif np.any(row == 1): 26 | result[1].append(index) 27 | else: 28 | raise ValueError("Order must be bipartite") 29 | 30 | return result 31 | 32 | def _make_order_from_bipartition(bipartition): 33 | order_size = len(bipartition[0]) + len(bipartition[1]) 34 | result = np.zeros((order_size, order_size), dtype=np.int8) 35 | for index in bipartition[0]: 36 | result[index, bipartition[1]] = -1 37 | result[bipartition[1], index] = 1 38 | 39 | return result 40 | 41 | class POMSet (object): 42 | """A Partially Ordered Multiset. 43 | 44 | A POMSet is composed of labels (the items in the multiset) and 45 | an order (the partial order of the labels). Partial orders are 46 | provided as 2 dimensional numpy ndarray specifying order relations 47 | on the `i`th and `j`th labels as 48 | order[i,j] == 1 <==> labels[i] > label[j] 49 | order[i,j] == 0 <==> label[i] is unrelated to label[j] 50 | order[i,j] == -1 <==> label[i] < label[j] 51 | 52 | The `size` of a POMSet is the number of labels. 53 | The `support` of a POMSet is the set of distinct labels. 54 | The `cardinality` of a POMSet is the size of the support. 55 | """ 56 | 57 | def __init__(self, labels=None, order=None, bipartition=None): 58 | 59 | if labels is not None: 60 | self.labels = np.array(labels, dtype=object) 61 | elif bipartition is not None: 62 | self.labels = np.hstack([np.array(bipartition[0]), 63 | np.array(bipartition[1])]) 64 | else: 65 | self.labels = np.array([], dtype=object) 66 | 67 | self.size = len(self.labels) 68 | self.support = set(self.labels) 69 | self.cardinality = len(self.support) 70 | 71 | self._is_unordered = False 72 | self._is_bipartite = False 73 | self._bipartition = None 74 | 75 | if bipartition is not None: 76 | assert(order is None) 77 | assert(sum(len(x) for x in bipartition) == len(self.labels)) 78 | self._is_bipartite = True 79 | self._bipartition = bipartition 80 | self.order = _make_order_from_bipartition(bipartition) 81 | 82 | elif order is not None: 83 | assert(order.shape[0] == len(self.labels)) 84 | self.order = order 85 | 86 | if np.all(self.order == 0): 87 | self._is_unordered = True 88 | 89 | if _is_bipartitite_order(self.order): 90 | self._is_bipartite = True 91 | self._bipartition = _get_bipartition(self.order) 92 | 93 | else: 94 | self.order = np.zeros((self.size, self.size), dtype=np.int8) 95 | self._is_unordered = True 96 | 97 | def multiplicity(self, element): 98 | """Return the number of occurences of `element` in the POMSet. 99 | 100 | Parameters 101 | ---------- 102 | 103 | element : object 104 | The object to query the multiplicity of. 105 | 106 | Returns 107 | ------- 108 | 109 | multiplicity : int 110 | The multiplicity of `element` in this POMSet. 111 | """ 112 | return np.sum(self.labels == element) 113 | 114 | def reverse_order(self): 115 | """Perform an in place order reversal on the POMSet. 116 | 117 | Thus if previously i > j, this method will result in 118 | i < j in the POMSet order. 119 | """ 120 | if not self._is_unordered: 121 | self.order = self.order.T 122 | 123 | def weakly_above(self, element, element_index=0): 124 | """Get all elements of the POMSet that are weakly above `element`. 125 | 126 | Here weakly above means elements that are either strictly greater than 127 | or unrelated to `element` in the POSET order. 128 | 129 | Parameters 130 | ---------- 131 | 132 | element : object 133 | The element of the POMSet to find elements above. 134 | 135 | element_index : int, optional 136 | In case there are multiple instances of element in the POMSet 137 | labels, the index of the element to find elements above; 138 | e.g. `element_index=3` will select the third copy of element 139 | within the label list. (default 0) 140 | 141 | Returns 142 | ------- 143 | 144 | labels_above : numpy ndarray 145 | A numpy array of label objects weakly above `element` 146 | """ 147 | if self._is_unordered: 148 | return self.labels.copy() 149 | 150 | label_index = np.where(self.labels == element)[0][element_index] 151 | 152 | if self._is_bipartite: 153 | if label_index in self._bipartition[0]: 154 | return self.labels.copy() 155 | else: 156 | return self.labels[self._bipartition[1]] 157 | 158 | return self.labels[~(self.order[label_index] == -1)] 159 | 160 | def _indices_strictly_above(self, element, element_index=0): 161 | if self._is_unordered: 162 | return np.array([], dtype=int) 163 | 164 | label_index = np.where(self.labels == element)[0][element_index] 165 | 166 | if self._is_bipartite: 167 | if label_index in self._bipartition[0]: 168 | return np.array(self._bipartition[1]) 169 | else: 170 | return np.array([], dtype=int) 171 | 172 | return np.where(self.order[label_index] == 1)[0] 173 | 174 | def strictly_above(self, element, element_index=0): 175 | """Get all elements of the POMSet that are strictly above `element`. 176 | 177 | Here weakly above means elements that are strictly greater than 178 | `element` in the POSET order. 179 | 180 | Parameters 181 | ---------- 182 | 183 | element : object 184 | The element of the POMSet to find elements above. 185 | 186 | element_index : int, optional 187 | In case there are multiple instances of element in the POMSet 188 | labels, the index of the element to find elements above; 189 | e.g. `element_index=3` will select the third copy of element 190 | within the label list. (default 0) 191 | 192 | Returns 193 | ------- 194 | 195 | labels_above : numpy ndarray 196 | A numpy array of label objects strictly above `element` 197 | """ 198 | if self._is_unordered: 199 | return np.array([], dtype=object) 200 | 201 | label_index = np.where(self.labels == element)[0][element_index] 202 | 203 | if self._is_bipartite: 204 | if label_index in self._bipartition[0]: 205 | return self.labels[self._bipartition[1]] 206 | else: 207 | return np.array([], dtype=object) 208 | 209 | return self.labels[(self.order[label_index] == 1)] 210 | 211 | def weakly_below(self, element, element_index=0): 212 | """Get all elements of the POMSet that are weakly below `element`. 213 | 214 | Here weakly above means elements that are either strictly less than 215 | or unrelated to `element` in the POSET order. 216 | 217 | Parameters 218 | ---------- 219 | 220 | element : object 221 | The element of the POMSet to find elements below. 222 | 223 | element_index : int, optional 224 | In case there are multiple instances of element in the POMSet 225 | labels, the index of the element to find elements below; 226 | e.g. `element_index=3` will select the third copy of element 227 | within the label list. (default 0) 228 | 229 | Returns 230 | ------- 231 | 232 | labels_below : numpy ndarray 233 | A numpy array of label objects weakly below `element` 234 | """ 235 | if self._is_unordered: 236 | return self.labels.copy() 237 | 238 | label_index = np.where(self.labels == element)[0][element_index] 239 | 240 | if self._is_bipartite: 241 | if label_index in self._bipartition[1]: 242 | return self.labels.copy() 243 | else: 244 | return self.labels[self._bipartition[0]] 245 | 246 | return self.labels[~(self.order[label_index] == 1)] 247 | 248 | def _indices_strictly_below(self, element, element_index=0): 249 | if self._is_unordered: 250 | return np.array([], dtype=int) 251 | 252 | label_index = np.where(self.labels == element)[0][element_index] 253 | 254 | if self._is_bipartite: 255 | if label_index in self._bipartition[1]: 256 | return self.labels[self._bipartition[0]] 257 | else: 258 | return np.array([], dtype=int) 259 | 260 | return np.where(self.order[label_index] == -1)[0] 261 | 262 | def strictly_below(self, element, element_index=0): 263 | """Get all elements of the POMSet that are strictly below `element`. 264 | 265 | Here weakly above means elements that are strictly less than 266 | `element` in the POSET order. 267 | 268 | Parameters 269 | ---------- 270 | 271 | element : object 272 | The element of the POMSet to find elements below. 273 | 274 | element_index : int, optional 275 | In case there are multiple instances of element in the POMSet 276 | labels, the index of the element to find elements below; 277 | e.g. `element_index=3` will select the third copy of element 278 | within the label list. (default 0) 279 | 280 | Returns 281 | ------- 282 | 283 | labels_below : numpy ndarray 284 | A numpy array of label objects strictly below `element` 285 | """ 286 | if self._is_unordered: 287 | return np.array([], dtype=object) 288 | 289 | label_index = np.where(self.labels == element)[0][element_index] 290 | 291 | if self._is_bipartite: 292 | if label_index in self._bipartition[1]: 293 | return self.labels[self._bipartition[0]] 294 | else: 295 | return np.array([], dtype=object) 296 | 297 | return self.labels[(self.order[label_index] == -1)] 298 | 299 | def weakly_greater_than(self, element1, element2, element1_index=0, element2_index=0): 300 | """Report whether `element1` is weakly greater than `element2`. 301 | 302 | In this case weakly greater than means not strictly less than. 303 | 304 | Parameters 305 | ---------- 306 | 307 | element1 : object 308 | The first element in the comparison 309 | 310 | element2 : object 311 | The second element in the comparison 312 | 313 | element1_index : int, optional 314 | In case there are multiple instances of element1 in the POMSet 315 | labels, the index of the element1 ; 316 | e.g. `element1_index=3` will select the third copy of element 317 | within the label list. (default 0) 318 | 319 | element2_index : int, optional 320 | In case there are multiple instances of element2 in the POMSet 321 | labels, the index of the element2 ; 322 | e.g. `element2_index=3` will select the third copy of element 323 | within the label list. (default 0) 324 | 325 | Returns 326 | ------- 327 | 328 | weakly_greater_than : boolean 329 | Whether `element1` is weakly greater than `element2` 330 | """ 331 | if self._is_unordered: 332 | return True 333 | label_index1 = np.where(self.labels == element1)[0][element1_index] 334 | label_index2 = np.where(self.labels == element2)[0][element2_index] 335 | return self.order[label_index1, label_index2] >= 0 336 | 337 | def strictly_greater_than(self, element1, element2, element1_index=0, element2_index=0): 338 | """Report whether `element1` is strictly greater than `element2`. 339 | 340 | Parameters 341 | ---------- 342 | 343 | element1 : object 344 | The first element in the comparison 345 | 346 | element2 : object 347 | The second element in the comparison 348 | 349 | element1_index : int, optional 350 | In case there are multiple instances of element1 in the POMSet 351 | labels, the index of the element1 ; 352 | e.g. `element1_index=3` will select the third copy of element 353 | within the label list. (default 0) 354 | 355 | element2_index : int, optional 356 | In case there are multiple instances of element2 in the POMSet 357 | labels, the index of the element2 ; 358 | e.g. `element2_index=3` will select the third copy of element 359 | within the label list. (default 0) 360 | 361 | Returns 362 | ------- 363 | 364 | strictly_greater_than : boolean 365 | Whether `element1` is strictly greater than `element2` 366 | """ 367 | if self._is_unordered: 368 | return False 369 | label_index1 = np.where(self.labels == element1)[0][element1_index] 370 | label_index2 = np.where(self.labels == element2)[0][element2_index] 371 | return self.order[label_index1, label_index2] > 0 372 | 373 | def weakly_less_than(self, element1, element2, element1_index=0, element2_index=0): 374 | """Report whether `element1` is weakly less than `element2`. 375 | 376 | In this case weakly less than means not strictly greater than. 377 | 378 | Parameters 379 | ---------- 380 | 381 | element1 : object 382 | The first element in the comparison 383 | 384 | element2 : object 385 | The second element in the comparison 386 | 387 | element1_index : int, optional 388 | In case there are multiple instances of element1 in the POMSet 389 | labels, the index of the element1 ; 390 | e.g. `element1_index=3` will select the third copy of element 391 | within the label list. (default 0) 392 | 393 | element2_index : int, optional 394 | In case there are multiple instances of element2 in the POMSet 395 | labels, the index of the element2 ; 396 | e.g. `element2_index=3` will select the third copy of element 397 | within the label list. (default 0) 398 | 399 | Returns 400 | ------- 401 | 402 | weakly_less_than : boolean 403 | Whether `element1` is weakly less than `element2` 404 | """ 405 | if self._is_unordered: 406 | return True 407 | label_index1 = np.where(self.labels == element1)[0][element1_index] 408 | label_index2 = np.where(self.labels == element2)[0][element2_index] 409 | return self.order[label_index1, label_index2] <= 0 410 | 411 | def strictly_less_than(self, element1, element2, element1_index=0, element2_index=0): 412 | """Report whether `element1` is strictly less than `element2`. 413 | 414 | Parameters 415 | ---------- 416 | 417 | element1 : object 418 | The first element in the comparison 419 | 420 | element2 : object 421 | The second element in the comparison 422 | 423 | element1_index : int, optional 424 | In case there are multiple instances of element1 in the POMSet 425 | labels, the index of the element1 ; 426 | e.g. `element1_index=3` will select the third copy of element 427 | within the label list. (default 0) 428 | 429 | element2_index : int, optional 430 | In case there are multiple instances of element2 in the POMSet 431 | labels, the index of the element2 ; 432 | e.g. `element2_index=3` will select the third copy of element 433 | within the label list. (default 0) 434 | 435 | Returns 436 | ------- 437 | 438 | strictly_less_than : boolean 439 | Whether `element1` is strictly less than `element2` 440 | """ 441 | if self._is_unordered: 442 | return False 443 | label_index1 = np.where(self.labels == element1)[0][element1_index] 444 | label_index2 = np.where(self.labels == element2)[0][element2_index] 445 | return self.order[label_index1, label_index2] < 0 446 | 447 | def add_label(self, new_label): 448 | """Add a new element to the POMSet. The added element will be 449 | unrelated to any other elements in the POMSet; to induce relations 450 | after using this method use the `add_dependency` or 451 | `add_dependencies_from` functions. 452 | 453 | Parameters 454 | ---------- 455 | 456 | new_label : object 457 | The new element to add to the POMSet. 458 | """ 459 | new_label_array = np.empty(self.size + 1, dtype=object) 460 | new_label_array[:-1] = self.labels 461 | del self.labels 462 | self.labels = new_label_array 463 | self.labels[-1] = new_label 464 | 465 | self.size = len(self.labels) 466 | self.support.add(new_label) 467 | self.cardinality = len(self.support) 468 | 469 | new_order = np.zeros((self.size, self.size), dtype=np.int8) 470 | if self.order.shape[0] > 0: 471 | new_order[:-1][:,:-1] = self.order 472 | del self.order 473 | self.order = new_order 474 | 475 | self._is_bipartite = False 476 | self._bipartition = None 477 | 478 | def add_dependency(self, from_label, to_label, from_index=0, to_index=0): 479 | """Add a new dependency relation to the POMSet. This states that 480 | `from_label` is strictly less than `to_label`. All other relations 481 | implicit from this will then be inferred and also added. 482 | 483 | Parameters 484 | ---------- 485 | 486 | from_label : object 487 | The lesser element of the new relation to add 488 | 489 | to_label : object 490 | The greater element of the new relation to add 491 | 492 | from_index : int, optional 493 | In case there are multiple instances of from_element in the POMSet 494 | labels, the index of the from_element ; 495 | e.g. `from_index=3` will select the third copy of from_element 496 | within the label list. (default 0) 497 | 498 | to_index : int, optional 499 | In case there are multiple instances of to_element in the POMSet 500 | labels, the index of the to_element ; 501 | e.g. `to_index=3` will select the third copy of to_element 502 | within the label list. (default 0) 503 | 504 | """ 505 | from_label_index = np.where(self.labels == from_label)[0][from_index] 506 | to_label_index = np.where(self.labels == to_label)[0][to_index] 507 | 508 | self.order[from_label_index, to_label_index] = -1 509 | self.order[to_label_index, from_label_index] = 1 510 | 511 | self.order[from_label_index, self._indices_strictly_above(to_label, to_index)] = -1 512 | self.order[to_label_index, self._indices_strictly_below(from_label, from_index)] = 1 513 | 514 | self._is_unordered = False 515 | 516 | if _is_bipartitite_order(self.order): 517 | self._is_bipartite = True 518 | self._bipartition = _get_bipartition(self.order) 519 | else: 520 | self._is_bipartite = False 521 | self._bipartition = None 522 | 523 | def add_labels_from(self, new_label_list): 524 | """ 525 | Add a number of new labels from an iterable of new labels. 526 | The added elements will be unrelated to any other elements 527 | in the POMSet. To add relations use the `add_dependency` or 528 | `add_dependencies_from` functions. 529 | 530 | Parameters 531 | ---------- 532 | 533 | new_label_list : iterable 534 | The new labels to be added 535 | """ 536 | labels_to_add = np.array(new_label_list) 537 | self.labels = np.hstack((self.labels, labels_to_add)) 538 | 539 | self.size = len(self.labels) 540 | self.support.update(new_label_list) 541 | self.cardinality = len(self.support) 542 | 543 | new_order = np.zeros((self.size, self.size), dtype=np.int8) 544 | new_order[:-1][:,:-1] = self.order 545 | del self.order 546 | self.order = new_order 547 | 548 | self._is_bipartite = False 549 | self._bipartition = None 550 | 551 | def add_dependencies_from(self, new_dependencies_list): 552 | """Add a number of new dependency relations from an iterable 553 | of dependencies. Each element of the iterable should be a tuple 554 | of 4 items: 555 | `(from_label, from_index, to_label, to_index)` 556 | See the documentation for `add_dependency` for more detail. 557 | 558 | Parameters 559 | ---------- 560 | 561 | new_dependencies_list : iterable 562 | The new dependences to be added, each dependency specified 563 | as a 4-tuple of `(from_label, from_index, to_label, to_index)`. 564 | """ 565 | for args in new_dependencies_list: 566 | self.add_dependency(args[0], args[2], args[1], args[3]) 567 | 568 | def remove_label(self, label_to_remove, label_index=0): 569 | """Remove a label from the POMSet, updating dependency 570 | relations accordingly in the POMSet order. 571 | 572 | Parameters 573 | ---------- 574 | 575 | label_to_remove : object 576 | The label to be removed from the POMSet. 577 | 578 | label_index : int, optional 579 | In case there are multiple instances of label_to_remove in the POMSet 580 | labels, the index of the label_to_remove ; 581 | e.g. `element_index=3` will select the third copy of label_to_remove 582 | within the label list. (default 0) 583 | """ 584 | label_to_remove_index = np.where(self.labels == label_to_remove)[0][label_index] 585 | selection = range(label_to_remove_index) + range(label_to_remove_index + 1, self.order.shape[0]) 586 | 587 | self.order = self.order[selection, :][:, selection] 588 | self.labels = self.labels[selection] 589 | 590 | def remove_dependency(self, from_label, to_label, from_index=0, to_index=0): 591 | """Remove a dependency from the POMSet. 592 | 593 | Parameters 594 | ---------- 595 | 596 | from_label : object 597 | The lower label of the dependency to be removed. 598 | 599 | to_label : object 600 | The upper label of the dependency to be removed. 601 | 602 | from_index : int, optional 603 | In case there are multiple instances of from_element in the POMSet 604 | labels, the index of the from_element ; 605 | e.g. `from_index=3` will select the third copy of from_element 606 | within the label list. (default 0) 607 | 608 | to_index : int, optional 609 | In case there are multiple instances of to_element in the POMSet 610 | labels, the index of the to_element ; 611 | e.g. `to_index=3` will select the third copy of to_element 612 | within the label list. (default 0) 613 | """ 614 | from_label_index = np.where(self.labels == from_label)[0][from_index] 615 | to_label_index = np.where(self.labels == to_label)[0][to_index] 616 | 617 | self.order[from_label_index, to_label_index] = 0 618 | self.order[to_label_index, from_label_index] = 0 619 | 620 | if np.all(self.order == 0): 621 | self._is_unordered = True 622 | 623 | if _is_bipartitite_order(self.order): 624 | self._is_bipartite = True 625 | self._bipartition = _get_bipartition(self.order) 626 | else: 627 | self._is_bipartite = False 628 | self._bipartition = None -------------------------------------------------------------------------------- /notebook/enron analysis.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "The main page containing the enron data can be found at: https://www.cs.cmu.edu/~./enron/\n" 8 | ] 9 | }, 10 | { 11 | "cell_type": "code", 12 | "execution_count": 178, 13 | "metadata": { 14 | "collapsed": false 15 | }, 16 | "outputs": [], 17 | "source": [ 18 | "import re\n", 19 | "import numpy as np\n", 20 | "import pandas as pd\n", 21 | "import email\n", 22 | "#Plotting stuff\n", 23 | "%matplotlib inline\n", 24 | "import matplotlib.pyplot as plt\n", 25 | "import seaborn as sns\n", 26 | "sns.set_context('poster')\n", 27 | "import hypergraph" 28 | ] 29 | }, 30 | { 31 | "cell_type": "markdown", 32 | "metadata": {}, 33 | "source": [ 34 | "Read the data into hyperedges. We preserve order only in so far as the first element in each array is the sender. Email addresses may appear multiple times if they were included multiple times in the header. For example their exist cases where a given address was included in both the cc and the bcc lines of the same message.\n", 35 | "\n", 36 | "to, cc and bcc addresses where treated the same and simply merged into a single list." 37 | ] 38 | }, 39 | { 40 | "cell_type": "code", 41 | "execution_count": 179, 42 | "metadata": { 43 | "collapsed": false, 44 | "scrolled": true 45 | }, 46 | "outputs": [], 47 | "source": [ 48 | "import os\n", 49 | "#for root, user, file in os.walk('/Users/jchealy/Downloads/maildir/'):\n", 50 | "root = '/Users/jchealy/Downloads/maildir/'\n", 51 | "count =0 \n", 52 | "edges = []\n", 53 | "file_index = []\n", 54 | "for user in os.listdir(root):\n", 55 | " #print(user)\n", 56 | " location = root+user+'/_sent_mail'\n", 57 | " if(count>2):\n", 58 | " break \n", 59 | " if(os.path.isdir(location)):\n", 60 | " #print(location)\n", 61 | " for fname in os.listdir(location):\n", 62 | " file= location+'/'+fname\n", 63 | " #print(file)\n", 64 | " with open(file) as f:\n", 65 | " message = email.message_from_file(f)\n", 66 | " edge = [message['from']]\n", 67 | " if 'To' in message:\n", 68 | " edge = edge+re.split(r'\\s*,\\s*', message['to'])\n", 69 | " if 'Cc' in message:\n", 70 | " edge = edge + re.split(r'\\s*,\\s*', message['cc'])\n", 71 | " if 'Bcc' in message:\n", 72 | " edge = edge + re.split(r'\\s*,\\s*', message['bcc'])\n", 73 | " edges.append(edge)\n", 74 | " file_index.append(file)" 75 | ] 76 | }, 77 | { 78 | "cell_type": "markdown", 79 | "metadata": {}, 80 | "source": [ 81 | "#Descriptive Statistics\n", 82 | "###Edge size distribution" 83 | ] 84 | }, 85 | { 86 | "cell_type": "code", 87 | "execution_count": 180, 88 | "metadata": { 89 | "collapsed": false 90 | }, 91 | "outputs": [ 92 | { 93 | "data": { 94 | "text/plain": [ 95 | "" 96 | ] 97 | }, 98 | "execution_count": 180, 99 | "metadata": {}, 100 | "output_type": "execute_result" 101 | }, 102 | { 103 | "data": { 104 | "image/png": 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SJNXTvPZJSCldDlxe5VokSZIkNQD3SZAkSZKUMe8dlyNiiLn3TZgA7gJ+A/w38LWUUsX7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\nGM33zPi4qc+fdq849Dw//OU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gfS3GXS/pjNLvSOBa4DzgCOAR4DpJP9hPbGZm3Y4nCWZm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\nzMzMzDr5L/F+yBetmpCZAAAAAElFTkSuQmCC\n", 105 | "text/plain": [ 106 | "" 107 | ] 108 | }, 109 | "metadata": {}, 110 | "output_type": "display_data" 111 | } 112 | ], 113 | "source": [ 114 | "l = pd.Series([len(x) for x in edges])\n", 115 | "d = l.value_counts().sort_index().reset_index()\n", 116 | "d.columns = ['index', 'freq']\n", 117 | "d['freq']=np.log10(d['freq'])\n", 118 | "ax = d.plot(x='index', y='freq', kind='scatter', alpha=0.6, xlim=[-10,max(d['index'])+10])\n", 119 | "ax.set_ylabel('Frequency (log10)')\n", 120 | "ax.set_xlabel('Hyperedge Size')" 121 | ] 122 | }, 123 | { 124 | "cell_type": "markdown", 125 | "metadata": {}, 126 | "source": [ 127 | "###Number of hyperedges in email hypergraph" 128 | ] 129 | }, 130 | { 131 | "cell_type": "code", 132 | "execution_count": 181, 133 | "metadata": { 134 | "collapsed": false 135 | }, 136 | "outputs": [ 137 | { 138 | "data": { 139 | "text/plain": [ 140 | "30109" 141 | ] 142 | }, 143 | "execution_count": 181, 144 | "metadata": {}, 145 | "output_type": "execute_result" 146 | } 147 | ], 148 | "source": [ 149 | "len(edges)" 150 | ] 151 | }, 152 | { 153 | "cell_type": "markdown", 154 | "metadata": {}, 155 | "source": [ 156 | "###Number of nodes in email hypergraph" 157 | ] 158 | }, 159 | { 160 | "cell_type": "code", 161 | "execution_count": 182, 162 | "metadata": { 163 | "collapsed": false 164 | }, 165 | "outputs": [ 166 | { 167 | "data": { 168 | "text/plain": [ 169 | "7568" 170 | ] 171 | }, 172 | "execution_count": 182, 173 | "metadata": {}, 174 | "output_type": "execute_result" 175 | } 176 | ], 177 | "source": [ 178 | "flat = [item for sublist in edges for item in sublist]\n", 179 | "len(flat)\n", 180 | "nodes = np.unique(flat)\n", 181 | "len(nodes)" 182 | ] 183 | }, 184 | { 185 | "cell_type": "markdown", 186 | "metadata": {}, 187 | "source": [ 188 | "###Next read the edges into Lelands library\n", 189 | "###Then write various output functions for these structures depending on folks want to ingest" 190 | ] 191 | }, 192 | { 193 | "cell_type": "code", 194 | "execution_count": 183, 195 | "metadata": { 196 | "collapsed": false 197 | }, 198 | "outputs": [ 199 | { 200 | "data": { 201 | "text/plain": [ 202 | "[['phillip.allen@enron.com', 'john.lavorato@enron.com'],\n", 203 | " ['phillip.allen@enron.com', 'leah.arsdall@enron.com'],\n", 204 | " ['phillip.allen@enron.com', 'randall.gay@enron.com'],\n", 205 | " ['phillip.allen@enron.com', 'greg.piper@enron.com'],\n", 206 | " ['phillip.allen@enron.com', 'greg.piper@enron.com'],\n", 207 | " ['phillip.allen@enron.com',\n", 208 | " 'david.l.johnson@enron.com',\n", 209 | " 'john.shafer@enron.com'],\n", 210 | " ['phillip.allen@enron.com', 'joyce.teixeira@enron.com'],\n", 211 | " ['phillip.allen@enron.com', 'mark.scott@enron.com'],\n", 212 | " ['phillip.allen@enron.com', 'zimam@enron.com']]" 213 | ] 214 | }, 215 | "execution_count": 183, 216 | "metadata": {}, 217 | "output_type": "execute_result" 218 | } 219 | ], 220 | "source": [ 221 | "edges[1:10]" 222 | ] 223 | }, 224 | { 225 | "cell_type": "markdown", 226 | "metadata": {}, 227 | "source": [ 228 | "###Pawel has requested that these addresses be remapped to one up integers and output in one array per line. To maximize code re-use I'll write that as function in the hypergraph library." 229 | ] 230 | }, 231 | { 232 | "cell_type": "markdown", 233 | "metadata": {}, 234 | "source": [ 235 | "###Ingest our array of arrays into a hypergraph object" 236 | ] 237 | }, 238 | { 239 | "cell_type": "code", 240 | "execution_count": 184, 241 | "metadata": { 242 | "collapsed": true 243 | }, 244 | "outputs": [], 245 | "source": [ 246 | "hg = hypergraph.Hypergraph()" 247 | ] 248 | }, 249 | { 250 | "cell_type": "code", 251 | "execution_count": 185, 252 | "metadata": { 253 | "collapsed": false 254 | }, 255 | "outputs": [ 256 | { 257 | "name": "stdout", 258 | "output_type": "stream", 259 | "text": [ 260 | "0\n", 261 | "10000\n", 262 | "20000\n", 263 | "30000\n" 264 | ] 265 | } 266 | ], 267 | "source": [ 268 | "for i, edge in enumerate(edges):\n", 269 | " hg.add_edge(i,edge)\n", 270 | " if(i%10000 == 0):\n", 271 | " print(i)" 272 | ] 273 | }, 274 | { 275 | "cell_type": "markdown", 276 | "metadata": {}, 277 | "source": [ 278 | "###Recompute the edge size distribution\n", 279 | "This is a quick example of how to access the hypergraph object." 280 | ] 281 | }, 282 | { 283 | "cell_type": "code", 284 | "execution_count": 186, 285 | "metadata": { 286 | "collapsed": false, 287 | "scrolled": false 288 | }, 289 | "outputs": [ 290 | { 291 | "data": { 292 | "text/plain": [ 293 | "" 294 | ] 295 | }, 296 | "execution_count": 186, 297 | "metadata": {}, 298 | "output_type": "execute_result" 299 | }, 300 | { 301 | "data": { 302 | "image/png": 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SJNXTvPZJSCldDlxe5VokSZIkNQD3SZAkSZKUMe8dlyNiiLn3TZgA7gJ+A/w38LWUUsX7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\nGM33zPi4qc+fdq849Dw//OU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303 | "text/plain": [ 304 | "" 305 | ] 306 | }, 307 | "metadata": {}, 308 | "output_type": "display_data" 309 | } 310 | ], 311 | "source": [ 312 | "edge_size = pd.Series([hg.edge[x].size for x in hg.edge])\n", 313 | "d = edge_size.value_counts().sort_index().reset_index()\n", 314 | "d.columns = ['index', 'freq']\n", 315 | "d['freq']=np.log10(d['freq'])\n", 316 | "ax = d.plot(x='index', y='freq', kind='scatter', alpha=0.6, xlim=[-10,max(d['index'])+10])\n", 317 | "ax.set_ylabel('Frequency (log10)')\n", 318 | "ax.set_xlabel('Hyperedge Size')" 319 | ] 320 | }, 321 | { 322 | "cell_type": "markdown", 323 | "metadata": {}, 324 | "source": [ 325 | "Now let's look at node size, which might be refered to as degree by some." 326 | ] 327 | }, 328 | { 329 | "cell_type": "code", 330 | "execution_count": 187, 331 | "metadata": { 332 | "collapsed": false, 333 | "scrolled": false 334 | }, 335 | "outputs": [ 336 | { 337 | "data": { 338 | "text/plain": [ 339 | "" 340 | ] 341 | }, 342 | "execution_count": 187, 343 | "metadata": {}, 344 | "output_type": "execute_result" 345 | }, 346 | { 347 | "data": { 348 | "image/png": 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B+CRJkiRVkELOwTgK+N4U178HrNq/cCRJkiRVskIKjMeAE6e4/nzgD/sXjiRJ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\nEMKGEML2EMKvQwh/PRvxSdJ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7e2nR6A/ok70+ofk47u6+d/e1yZq8O7s2sm1bLw88uJma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\np9V3NWFYT+pQnD8TegbKgKvc/b2OXpy7L3b369z9U9F5v0o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349 | "text/plain": [ 350 | "" 351 | ] 352 | }, 353 | "metadata": {}, 354 | "output_type": "display_data" 355 | } 356 | ], 357 | "source": [ 358 | "node_size = pd.Series([hg.node[x].size for x in hg.node])\n", 359 | "d = node_size.value_counts().sort_index().reset_index()\n", 360 | "d.columns = ['index', 'freq']\n", 361 | "d['freq']=np.log10(d['freq'])\n", 362 | "d['index']=np.log10(d['index'])\n", 363 | "ax = d.plot(x='index', y='freq', kind='scatter', alpha=0.6, xlim=[-1,max(d['index'])+1])\n", 364 | "ax.set_ylabel('Frequency (log10)')\n", 365 | "ax.set_xlabel('Vertex Size (log10)')" 366 | ] 367 | }, 368 | { 369 | "cell_type": "markdown", 370 | "metadata": {}, 371 | "source": [ 372 | "### We can look at sender degree (number of emails sent by an individual) since the sender is currently coded as the first vertex in every hyperedge" 373 | ] 374 | }, 375 | { 376 | "cell_type": "code", 377 | "execution_count": 188, 378 | "metadata": { 379 | "collapsed": false, 380 | "scrolled": true 381 | }, 382 | "outputs": [ 383 | { 384 | "data": { 385 | "text/plain": [ 386 | "0 phillip.allen@enron.com\n", 387 | "1 phillip.allen@enron.com\n", 388 | "2 phillip.allen@enron.com\n", 389 | "3 phillip.allen@enron.com\n", 390 | "4 phillip.allen@enron.com\n", 391 | "dtype: object" 392 | ] 393 | }, 394 | "execution_count": 188, 395 | "metadata": {}, 396 | "output_type": "execute_result" 397 | } 398 | ], 399 | "source": [ 400 | "sender = pd.Series([hg.edge[x].labels[0] for x in hg.edge])\n", 401 | "sender.head()" 402 | ] 403 | }, 404 | { 405 | "cell_type": "code", 406 | "execution_count": 189, 407 | "metadata": { 408 | "collapsed": false 409 | }, 410 | "outputs": [ 411 | { 412 | "data": { 413 | "text/plain": [ 414 | "" 415 | ] 416 | }, 417 | "execution_count": 189, 418 | "metadata": {}, 419 | "output_type": "execute_result" 420 | }, 421 | { 422 | "data": { 423 | "image/png": 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azdzz1GKeeHkFbRmDtktKYL9Jw9lv0jDCpOFM3WsI5a7ALUmStMcxUPTQnhoo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\n8fV5239B0hXly0DTawA8H2N8X1tvNIQwGRhDcsc93ydJ7vIfFWN8MXf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424 | "text/plain": [ 425 | "" 426 | ] 427 | }, 428 | "metadata": {}, 429 | "output_type": "display_data" 430 | } 431 | ], 432 | "source": [ 433 | "sender = pd.Series([hg.edge[x].labels[0] for x in hg.edge])\n", 434 | "d = sender.value_counts().plot(kind='line', title='number of email sent by each user', logx=False, logy=True)\n", 435 | "plt.xticks([])\n", 436 | "plt.ylabel('outgoing hyperedges')\n", 437 | "plt.xlabel('sender (decreasing order)')" 438 | ] 439 | }, 440 | { 441 | "cell_type": "markdown", 442 | "metadata": {}, 443 | "source": [ 444 | "Might be worth inducing the 2 section and overlaying the two degree distributions on each other." 445 | ] 446 | }, 447 | { 448 | "cell_type": "markdown", 449 | "metadata": {}, 450 | "source": [ 451 | "### The cardinality of an edge is the number of unique nodes in the edge. An interesting question might be which email have a cardinality which differs from their size. " 452 | ] 453 | }, 454 | { 455 | "cell_type": "code", 456 | "execution_count": 194, 457 | "metadata": { 458 | "collapsed": true 459 | }, 460 | "outputs": [], 461 | "source": [ 462 | "pd.set_option('precision',2)" 463 | ] 464 | }, 465 | { 466 | "cell_type": "code", 467 | "execution_count": 203, 468 | "metadata": { 469 | "collapsed": false 470 | }, 471 | "outputs": [ 472 | { 473 | "name": "stdout", 474 | "output_type": "stream", 475 | "text": [ 476 | "4966 out of 30109 (16.49%) edges differed between cardinality and size\n" 477 | ] 478 | } 479 | ], 480 | "source": [ 481 | "edge_size = pd.Series([hg.edge[x].size for x in hg.edge])\n", 482 | "edge_card = pd.Series([hg.edge[x].cardinality for x in hg.edge])\n", 483 | "#hg.edge[[edge_size!=edge_card]]\n", 484 | "edge_difference_index = np.where(edge_size!=edge_card)[0]\n", 485 | "print(str(len(edge_difference_index))+\" out of \" + str(len(edge_size)) + \" (\"+\n", 486 | " \"{:.2f}\".format(len(edge_difference_index)/len(edge_size)*100)+\n", 487 | " \"%) edges differed between cardinality and size\")" 488 | ] 489 | }, 490 | { 491 | "cell_type": "code", 492 | "execution_count": 207, 493 | "metadata": { 494 | "collapsed": false, 495 | "scrolled": false 496 | }, 497 | "outputs": [ 498 | { 499 | "data": { 500 | "text/plain": [ 501 | "[array(['phillip.allen@enron.com', 'brad.mcsherry@enron.com',\n", 502 | " 'john.lavorato@enron.com', 'hunter.shively@enron.com',\n", 503 | " 'john.lavorato@enron.com', 'hunter.shively@enron.com'], dtype=object),\n", 504 | " array(['phillip.allen@enron.com', 'tim.heizenrader@enron.com',\n", 505 | " 'tim.belden@enron.com', 'tim.belden@enron.com'], dtype=object),\n", 506 | " array(['phillip.allen@enron.com', 'ned.higgins@enron.com',\n", 507 | " 'mike.grigsby@enron.com', 'mike.grigsby@enron.com'], dtype=object),\n", 508 | " array(['phillip.allen@enron.com', 'tara.sweitzer@enron.com',\n", 509 | " 'brenda.flores-cuellar@enron.com', 'brenda.flores-cuellar@enron.com'], dtype=object),\n", 510 | " array(['phillip.allen@enron.com', 'brenda.flores-cuellar@enron.com',\n", 511 | " 'dale.neuner@enron.com', 'dale.neuner@enron.com'], dtype=object)]" 512 | ] 513 | }, 514 | "execution_count": 207, 515 | "metadata": {}, 516 | "output_type": "execute_result" 517 | } 518 | ], 519 | "source": [ 520 | "[hg.edge[x].labels for x in edge_difference_index][:5]" 521 | ] 522 | }, 523 | { 524 | "cell_type": "markdown", 525 | "metadata": {}, 526 | "source": [ 527 | "###Output in basic integer tuple format\n", 528 | "I'll convert this into a utility function directly in the library next" 529 | ] 530 | }, 531 | { 532 | "cell_type": "code", 533 | "execution_count": 49, 534 | "metadata": { 535 | "collapsed": false 536 | }, 537 | "outputs": [], 538 | "source": [ 539 | "keys = hg.nodes\n", 540 | "values = range(len(hg.nodes))\n", 541 | "vertex_map = dict(zip(keys,values))\n", 542 | "\n", 543 | "filename = \"enronNumericHypergraphEdgelist.txt\"\n", 544 | "file = open(filename,'w')\n", 545 | "@np.vectorize\n", 546 | "def vertex_mapper(x):\n", 547 | " return vertex_map[x]\n", 548 | "\n", 549 | "for e in hg.edge:\n", 550 | " tup = vertex_mapper(hg.edge[e].labels)\n", 551 | " file.write(\" \".join(str(elem) for elem in tup)+\"\\n\")\n", 552 | " #print(\" \".join(str(elem) for elem in [vertex_map[x] for x in tup]))\n", 553 | "file.close() " 554 | ] 555 | }, 556 | { 557 | "cell_type": "code", 558 | "execution_count": 33, 559 | "metadata": { 560 | "collapsed": false 561 | }, 562 | "outputs": [ 563 | { 564 | "data": { 565 | "text/plain": [ 566 | "array([0, 128, 128, 153, 168, 186, 269, 277, 297, 297, 324, 453, 589, 1416,\n", 567 | " 1418, 1418, 1419, 1433, 1436, 1459, 1462, 1463, 1464, 1466, 3592,\n", 568 | " 3594, 3943, 4850, 4875, 4885, 4898, 4909, 4912, 4915, 4917, 4919,\n", 569 | " 4929, 4929, 4931, 4944, 4946, 4948, 4956, 4957, 4980, 4980, 4984,\n", 570 | " 4986, 4998, 5009, 5040, 5044, 5048, 5048, 5074, 5081, 5081, 5118,\n", 571 | " 5119, 5147, 5167, 5168, 5170, 5181, 5186, 5228, 5230, 5266, 5329,\n", 572 | " 5336, 5339, 5347, 5347, 5357, 5369, 5373, 5385, 5386, 5391, 5404,\n", 573 | " 5406, 5430, 5438, 5511, 5554, 5571, 5594, 5639, 5639, 5715, 10885,\n", 574 | " 11014, 11041, 11041, 11068, 11068, 11223, 11225, 11227, 11234,\n", 575 | " 11234, 11235, 11237, 11237, 11239, 11240, 11240, 11248, 11258,\n", 576 | " 11260, 11260, 11268, 11271, 11277, 11278, 11280, 11282, 11282,\n", 577 | " 11294, 11295, 11295, 11304, 11320, 11325, 11337, 11340, 11341,\n", 578 | " 11346, 11352, 11354, 11366, 11367, 11367, 11368, 11368, 11370,\n", 579 | " 11370, 11373, 11374, 11374, 11387, 11387, 11412, 11417, 11418,\n", 580 | " 11418, 11425, 11434, 11436, 11440, 11440, 11443, 11443, 11449,\n", 581 | " 11460, 11462, 11463, 11463, 11466, 11470, 11471, 11487, 11495,\n", 582 | " 11544, 11545, 11565, 12858, 15992, 15999, 16017, 16019, 16034,\n", 583 | " 16052, 16052, 16052, 16052, 16068, 16087, 16105, 16120, 16140,\n", 584 | " 16177, 16182, 16187, 16218, 16252, 16261, 16311, 16324, 16331,\n", 585 | " 16374, 16393, 16403, 16432, 16531, 23900, 27889, 27906, 27913,\n", 586 | " 27913, 27913, 27931, 28106, 28178, 28181, 28676, 28696, 28712,\n", 587 | " 28736, 28755, 28759, 28776, 28777, 28780, 28791, 28819, 28866,\n", 588 | " 28958, 29018, 29174, 29204, 29205, 29941], dtype=object)" 589 | ] 590 | }, 591 | "execution_count": 33, 592 | "metadata": {}, 593 | "output_type": "execute_result" 594 | } 595 | ], 596 | "source": [ 597 | "hg.node['tim.belden@enron.com'].labels" 598 | ] 599 | }, 600 | { 601 | "cell_type": "code", 602 | "execution_count": null, 603 | "metadata": { 604 | "collapsed": true 605 | }, 606 | "outputs": [], 607 | "source": [] 608 | } 609 | ], 610 | "metadata": { 611 | "kernelspec": { 612 | "display_name": "Python 3", 613 | "language": "python", 614 | "name": "python3" 615 | }, 616 | "language_info": { 617 | "codemirror_mode": { 618 | "name": "ipython", 619 | "version": 3 620 | }, 621 | "file_extension": ".py", 622 | "mimetype": "text/x-python", 623 | "name": "python", 624 | "nbconvert_exporter": "python", 625 | "pygments_lexer": "ipython3", 626 | "version": "3.4.3" 627 | } 628 | }, 629 | "nbformat": 4, 630 | "nbformat_minor": 0 631 | } 632 | -------------------------------------------------------------------------------- /setup.py: -------------------------------------------------------------------------------- 1 | from setuptools import setup 2 | 3 | def readme(): 4 | with open('README.rst') as readme_file: 5 | return readme_file.read() 6 | 7 | configuration = { 8 | 'name' : 'hypergraph', 9 | 'version' : '0.1', 10 | 'description' : 'Hypergraph tools and algorithms', 11 | 'long_description' : readme(), 12 | 'classifiers' : [ 13 | 'Development Status :: 3 - Alpha', 14 | 'Intended Audience :: Science/Research', 15 | 'Intended Audience :: Developers', 16 | 'License :: OSI Approved', 17 | 'Programming Language :: Python', 18 | 'Topic :: Software Development', 19 | 'Topic :: Scientific/Engineering', 20 | 'Operating System :: Microsoft :: Windows', 21 | 'Operating System :: POSIX', 22 | 'Operating System :: Unix', 23 | 'Operating System :: MacOS', 24 | 'Programming Language :: Python :: 2.7', 25 | 'Programming Language :: Python :: 3.4', 26 | ], 27 | 'keywords' : 'hypergraph graph network community pomset', 28 | 'url' : 'http://github.com/lmcinnes/hypergrapg', 29 | 'maintainer' : 'Leland McInnes', 30 | 'maintainer_email' : 'leland.mcinnes@gmail.com', 31 | 'license' : 'BSD', 32 | 'packages' : ['hypergraph'], 33 | 'install_requires' : ['numpy>=1.5', 34 | 'networkx>=1.9.1'], 35 | 'ext_modules' : [], 36 | 'test_suite' : 'nose.collector', 37 | 'tests_require' : ['nose'], 38 | } 39 | 40 | setup(**configuration) 41 | --------------------------------------------------------------------------------