Warning

This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

"""
"""

from __future__ import division

import math

import networkx as nx
from networkx.utils.decorators import *

__all__ = ['resource_allocation_index',
'jaccard_coefficient',
'preferential_attachment',
'cn_soundarajan_hopcroft',
'ra_index_soundarajan_hopcroft',
'within_inter_cluster']

@not_implemented_for('directed')
@not_implemented_for('multigraph')
[docs]def resource_allocation_index(G, ebunch=None): r"""Compute the resource allocation index of all node pairs in ebunch. Resource allocation index of u and v is defined as .. math:: \sum_{w \in \Gamma(u) \cap \Gamma(v)} \frac{1}{|\Gamma(w)|} where :math:\Gamma(u) denotes the set of neighbors of u. Parameters ---------- G : graph A NetworkX undirected graph. ebunch : iterable of node pairs, optional (default = None) Resource allocation index will be computed for each pair of nodes given in the iterable. The pairs must be given as 2-tuples (u, v) where u and v are nodes in the graph. If ebunch is None then all non-existent edges in the graph will be used. Default value: None. Returns ------- piter : iterator An iterator of 3-tuples in the form (u, v, p) where (u, v) is a pair of nodes and p is their resource allocation index. Examples -------- >>> import networkx as nx >>> G = nx.complete_graph(5) >>> preds = nx.resource_allocation_index(G, [(0, 1), (2, 3)]) >>> for u, v, p in preds: ... '(%d, %d) -> %.8f' % (u, v, p) ... '(0, 1) -> 0.75000000' '(2, 3) -> 0.75000000' References ---------- .. [1] T. Zhou, L. Lu, Y.-C. Zhang. Predicting missing links via local information. Eur. Phys. J. B 71 (2009) 623. http://arxiv.org/pdf/0901.0553.pdf """ if ebunch is None: ebunch = nx.non_edges(G) def predict(u, v): return sum(1 / G.degree(w) for w in nx.common_neighbors(G, u, v)) return ((u, v, predict(u, v)) for u, v in ebunch)
@not_implemented_for('directed') @not_implemented_for('multigraph')
[docs]def jaccard_coefficient(G, ebunch=None): r"""Compute the Jaccard coefficient of all node pairs in ebunch. Jaccard coefficient of nodes u and v is defined as .. math:: \frac{|\Gamma(u) \cap \Gamma(v)|}{|\Gamma(u) \cup \Gamma(v)|} where :math:\Gamma(u) denotes the set of neighbors of u. Parameters ---------- G : graph A NetworkX undirected graph. ebunch : iterable of node pairs, optional (default = None) Jaccard coefficient will be computed for each pair of nodes given in the iterable. The pairs must be given as 2-tuples (u, v) where u and v are nodes in the graph. If ebunch is None then all non-existent edges in the graph will be used. Default value: None. Returns ------- piter : iterator An iterator of 3-tuples in the form (u, v, p) where (u, v) is a pair of nodes and p is their Jaccard coefficient. Examples -------- >>> import networkx as nx >>> G = nx.complete_graph(5) >>> preds = nx.jaccard_coefficient(G, [(0, 1), (2, 3)]) >>> for u, v, p in preds: ... '(%d, %d) -> %.8f' % (u, v, p) ... '(0, 1) -> 0.60000000' '(2, 3) -> 0.60000000' References ---------- .. [1] D. Liben-Nowell, J. Kleinberg. The Link Prediction Problem for Social Networks (2004). http://www.cs.cornell.edu/home/kleinber/link-pred.pdf """ if ebunch is None: ebunch = nx.non_edges(G) def predict(u, v): cnbors = list(nx.common_neighbors(G, u, v)) union_size = len(set(G[u]) | set(G[v])) if union_size == 0: return 0 else: return len(cnbors) / union_size return ((u, v, predict(u, v)) for u, v in ebunch)
@not_implemented_for('directed') @not_implemented_for('multigraph')
[docs]def adamic_adar_index(G, ebunch=None): r"""Compute the Adamic-Adar index of all node pairs in ebunch. Adamic-Adar index of u and v is defined as .. math:: \sum_{w \in \Gamma(u) \cap \Gamma(v)} \frac{1}{\log |\Gamma(w)|} where :math:\Gamma(u) denotes the set of neighbors of u. Parameters ---------- G : graph NetworkX undirected graph. ebunch : iterable of node pairs, optional (default = None) Adamic-Adar index will be computed for each pair of nodes given in the iterable. The pairs must be given as 2-tuples (u, v) where u and v are nodes in the graph. If ebunch is None then all non-existent edges in the graph will be used. Default value: None. Returns ------- piter : iterator An iterator of 3-tuples in the form (u, v, p) where (u, v) is a pair of nodes and p is their Adamic-Adar index. Examples -------- >>> import networkx as nx >>> G = nx.complete_graph(5) >>> preds = nx.adamic_adar_index(G, [(0, 1), (2, 3)]) >>> for u, v, p in preds: ... '(%d, %d) -> %.8f' % (u, v, p) ... '(0, 1) -> 2.16404256' '(2, 3) -> 2.16404256' References ---------- .. [1] D. Liben-Nowell, J. Kleinberg. The Link Prediction Problem for Social Networks (2004). http://www.cs.cornell.edu/home/kleinber/link-pred.pdf """ if ebunch is None: ebunch = nx.non_edges(G) def predict(u, v): return sum(1 / math.log(G.degree(w)) for w in nx.common_neighbors(G, u, v)) return ((u, v, predict(u, v)) for u, v in ebunch)
@not_implemented_for('directed') @not_implemented_for('multigraph')
[docs]def preferential_attachment(G, ebunch=None): r"""Compute the preferential attachment score of all node pairs in ebunch. Preferential attachment score of u and v is defined as .. math:: |\Gamma(u)| |\Gamma(v)| where :math:\Gamma(u) denotes the set of neighbors of u. Parameters ---------- G : graph NetworkX undirected graph. ebunch : iterable of node pairs, optional (default = None) Preferential attachment score will be computed for each pair of nodes given in the iterable. The pairs must be given as 2-tuples (u, v) where u and v are nodes in the graph. If ebunch is None then all non-existent edges in the graph will be used. Default value: None. Returns ------- piter : iterator An iterator of 3-tuples in the form (u, v, p) where (u, v) is a pair of nodes and p is their preferential attachment score. Examples -------- >>> import networkx as nx >>> G = nx.complete_graph(5) >>> preds = nx.preferential_attachment(G, [(0, 1), (2, 3)]) >>> for u, v, p in preds: ... '(%d, %d) -> %d' % (u, v, p) ... '(0, 1) -> 16' '(2, 3) -> 16' References ---------- .. [1] D. Liben-Nowell, J. Kleinberg. The Link Prediction Problem for Social Networks (2004). http://www.cs.cornell.edu/home/kleinber/link-pred.pdf """ if ebunch is None: ebunch = nx.non_edges(G) return ((u, v, G.degree(u) * G.degree(v)) for u, v in ebunch)
@not_implemented_for('directed') @not_implemented_for('multigraph')
[docs]def cn_soundarajan_hopcroft(G, ebunch=None, community='community'): r"""Count the number of common neighbors of all node pairs in ebunch using community information. For two nodes u and v, this function computes the number of common neighbors and bonus one for each common neighbor belonging to the same community as u and v. Mathematically, .. math:: |\Gamma(u) \cap \Gamma(v)| + \sum_{w \in \Gamma(u) \cap \Gamma(v)} f(w) where f(w) equals 1 if w belongs to the same community as u and v or 0 otherwise and :math:\Gamma(u) denotes the set of neighbors of u. Parameters ---------- G : graph A NetworkX undirected graph. ebunch : iterable of node pairs, optional (default = None) The score will be computed for each pair of nodes given in the iterable. The pairs must be given as 2-tuples (u, v) where u and v are nodes in the graph. If ebunch is None then all non-existent edges in the graph will be used. Default value: None. community : string, optional (default = 'community') Nodes attribute name containing the community information. G[u][community] identifies which community u belongs to. Each node belongs to at most one community. Default value: 'community'. Returns ------- piter : iterator An iterator of 3-tuples in the form (u, v, p) where (u, v) is a pair of nodes and p is their score. Examples -------- >>> import networkx as nx >>> G = nx.path_graph(3) >>> G.node[0]['community'] = 0 >>> G.node[1]['community'] = 0 >>> G.node[2]['community'] = 0 >>> preds = nx.cn_soundarajan_hopcroft(G, [(0, 2)]) >>> for u, v, p in preds: ... '(%d, %d) -> %d' % (u, v, p) ... '(0, 2) -> 2' References ---------- .. [1] Sucheta Soundarajan and John Hopcroft. Using community information to improve the precision of link prediction methods. In Proceedings of the 21st international conference companion on World Wide Web (WWW '12 Companion). ACM, New York, NY, USA, 607-608. http://doi.acm.org/10.1145/2187980.2188150 """ if ebunch is None: ebunch = nx.non_edges(G) def predict(u, v): Cu = _community(G, u, community) Cv = _community(G, v, community) cnbors = list(nx.common_neighbors(G, u, v)) if Cu == Cv: return len(cnbors) + sum(_community(G, w, community) == Cu for w in cnbors) else: return len(cnbors) return ((u, v, predict(u, v)) for u, v in ebunch)
@not_implemented_for('directed') @not_implemented_for('multigraph')
[docs]def ra_index_soundarajan_hopcroft(G, ebunch=None, community='community'): r"""Compute the resource allocation index of all node pairs in ebunch using community information. For two nodes u and v, this function computes the resource allocation index considering only common neighbors belonging to the same community as u and v. Mathematically, .. math:: \sum_{w \in \Gamma(u) \cap \Gamma(v)} \frac{f(w)}{|\Gamma(w)|} where f(w) equals 1 if w belongs to the same community as u and v or 0 otherwise and :math:\Gamma(u) denotes the set of neighbors of u. Parameters ---------- G : graph A NetworkX undirected graph. ebunch : iterable of node pairs, optional (default = None) The score will be computed for each pair of nodes given in the iterable. The pairs must be given as 2-tuples (u, v) where u and v are nodes in the graph. If ebunch is None then all non-existent edges in the graph will be used. Default value: None. community : string, optional (default = 'community') Nodes attribute name containing the community information. G[u][community] identifies which community u belongs to. Each node belongs to at most one community. Default value: 'community'. Returns ------- piter : iterator An iterator of 3-tuples in the form (u, v, p) where (u, v) is a pair of nodes and p is their score. Examples -------- >>> import networkx as nx >>> G = nx.Graph() >>> G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3)]) >>> G.node[0]['community'] = 0 >>> G.node[1]['community'] = 0 >>> G.node[2]['community'] = 1 >>> G.node[3]['community'] = 0 >>> preds = nx.ra_index_soundarajan_hopcroft(G, [(0, 3)]) >>> for u, v, p in preds: ... '(%d, %d) -> %.8f' % (u, v, p) ... '(0, 3) -> 0.50000000' References ---------- .. [1] Sucheta Soundarajan and John Hopcroft. Using community information to improve the precision of link prediction methods. In Proceedings of the 21st international conference companion on World Wide Web (WWW '12 Companion). ACM, New York, NY, USA, 607-608. http://doi.acm.org/10.1145/2187980.2188150 """ if ebunch is None: ebunch = nx.non_edges(G) def predict(u, v): Cu = _community(G, u, community) Cv = _community(G, v, community) if Cu == Cv: cnbors = nx.common_neighbors(G, u, v) return sum(1 / G.degree(w) for w in cnbors if _community(G, w, community) == Cu) else: return 0 return ((u, v, predict(u, v)) for u, v in ebunch)
@not_implemented_for('directed') @not_implemented_for('multigraph')
[docs]def within_inter_cluster(G, ebunch=None, delta=0.001, community='community'): """Compute the ratio of within- and inter-cluster common neighbors of all node pairs in ebunch. For two nodes u and v, if a common neighbor w belongs to the same community as them, w is considered as within-cluster common neighbor of u and v. Otherwise, it is considered as inter-cluster common neighbor of u and v. The ratio between the size of the set of within- and inter-cluster common neighbors is defined as the WIC measure. [1]_ Parameters ---------- G : graph A NetworkX undirected graph. ebunch : iterable of node pairs, optional (default = None) The WIC measure will be computed for each pair of nodes given in the iterable. The pairs must be given as 2-tuples (u, v) where u and v are nodes in the graph. If ebunch is None then all non-existent edges in the graph will be used. Default value: None. delta : float, optional (default = 0.001) Value to prevent division by zero in case there is no inter-cluster common neighbor between two nodes. See [1]_ for details. Default value: 0.001. community : string, optional (default = 'community') Nodes attribute name containing the community information. G[u][community] identifies which community u belongs to. Each node belongs to at most one community. Default value: 'community'. Returns ------- piter : iterator An iterator of 3-tuples in the form (u, v, p) where (u, v) is a pair of nodes and p is their WIC measure. Examples -------- >>> import networkx as nx >>> G = nx.Graph() >>> G.add_edges_from([(0, 1), (0, 2), (0, 3), (1, 4), (2, 4), (3, 4)]) >>> G.node[0]['community'] = 0 >>> G.node[1]['community'] = 1 >>> G.node[2]['community'] = 0 >>> G.node[3]['community'] = 0 >>> G.node[4]['community'] = 0 >>> preds = nx.within_inter_cluster(G, [(0, 4)]) >>> for u, v, p in preds: ... '(%d, %d) -> %.8f' % (u, v, p) ... '(0, 4) -> 1.99800200' >>> preds = nx.within_inter_cluster(G, [(0, 4)], delta=0.5) >>> for u, v, p in preds: ... '(%d, %d) -> %.8f' % (u, v, p) ... '(0, 4) -> 1.33333333' References ---------- .. [1] Jorge Carlos Valverde-Rebaza and Alneu de Andrade Lopes. Link prediction in complex networks based on cluster information. In Proceedings of the 21st Brazilian conference on Advances in Artificial Intelligence (SBIA'12) http://dx.doi.org/10.1007/978-3-642-34459-6_10 """ if delta <= 0: raise nx.NetworkXAlgorithmError('Delta must be greater than zero') if ebunch is None: ebunch = nx.non_edges(G) def predict(u, v): Cu = _community(G, u, community) Cv = _community(G, v, community) if Cu == Cv: cnbors = set(nx.common_neighbors(G, u, v)) within = set(w for w in cnbors if _community(G, w, community) == Cu) inter = cnbors - within return len(within) / (len(inter) + delta) else: return 0 return ((u, v, predict(u, v)) for u, v in ebunch)
def _community(G, u, community): """Get the community of the given node.""" node_u = G.node[u] try: return node_u[community] except KeyError: raise nx.NetworkXAlgorithmError('No community information')