Mercurial > repos > shellac > sam_consensus_v3
diff env/lib/python3.9/site-packages/networkx/algorithms/centrality/group.py @ 0:4f3585e2f14b draft default tip
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
| author | shellac |
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| date | Mon, 22 Mar 2021 18:12:50 +0000 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/env/lib/python3.9/site-packages/networkx/algorithms/centrality/group.py Mon Mar 22 18:12:50 2021 +0000 @@ -0,0 +1,366 @@ +"""Group centrality measures.""" +from itertools import combinations + + +import networkx as nx +from networkx.utils.decorators import not_implemented_for + + +__all__ = [ + "group_betweenness_centrality", + "group_closeness_centrality", + "group_degree_centrality", + "group_in_degree_centrality", + "group_out_degree_centrality", +] + + +def group_betweenness_centrality(G, C, normalized=True, weight=None): + r"""Compute the group betweenness centrality for a group of nodes. + + Group betweenness centrality of a group of nodes $C$ is the sum of the + fraction of all-pairs shortest paths that pass through any vertex in $C$ + + .. math:: + + c_B(C) =\sum_{s,t \in V-C; s<t} \frac{\sigma(s, t|C)}{\sigma(s, t)} + + where $V$ is the set of nodes, $\sigma(s, t)$ is the number of + shortest $(s, t)$-paths, and $\sigma(s, t|C)$ is the number of + those paths passing through some node in group $C$. Note that + $(s, t)$ are not members of the group ($V-C$ is the set of nodes + in $V$ that are not in $C$). + + Parameters + ---------- + G : graph + A NetworkX graph. + + C : list or set + C is a group of nodes which belong to G, for which group betweenness + centrality is to be calculated. + + normalized : bool, optional + If True, group betweenness is normalized by `2/((|V|-|C|)(|V|-|C|-1))` + for graphs and `1/((|V|-|C|)(|V|-|C|-1))` for directed graphs where `|V|` + is the number of nodes in G and `|C|` is the number of nodes in C. + + weight : None or string, optional (default=None) + If None, all edge weights are considered equal. + Otherwise holds the name of the edge attribute used as weight. + + Raises + ------ + NodeNotFound + If node(s) in C are not present in G. + + Returns + ------- + betweenness : float + Group betweenness centrality of the group C. + + See Also + -------- + betweenness_centrality + + Notes + ----- + The measure is described in [1]_. + The algorithm is an extension of the one proposed by Ulrik Brandes for + betweenness centrality of nodes. Group betweenness is also mentioned in + his paper [2]_ along with the algorithm. The importance of the measure is + discussed in [3]_. + + The number of nodes in the group must be a maximum of n - 2 where `n` + is the total number of nodes in the graph. + + For weighted graphs the edge weights must be greater than zero. + Zero edge weights can produce an infinite number of equal length + paths between pairs of nodes. + + References + ---------- + .. [1] M G Everett and S P Borgatti: + The Centrality of Groups and Classes. + Journal of Mathematical Sociology. 23(3): 181-201. 1999. + http://www.analytictech.com/borgatti/group_centrality.htm + .. [2] Ulrik Brandes: + On Variants of Shortest-Path Betweenness + Centrality and their Generic Computation. + Social Networks 30(2):136-145, 2008. + http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.72.9610&rep=rep1&type=pdf + .. [3] Sourav Medya et. al.: + Group Centrality Maximization via Network Design. + SIAM International Conference on Data Mining, SDM 2018, 126–134. + https://sites.cs.ucsb.edu/~arlei/pubs/sdm18.pdf + """ + betweenness = 0 # initialize betweenness to 0 + V = set(G) # set of nodes in G + C = set(C) # set of nodes in C (group) + if len(C - V) != 0: # element(s) of C not in V + raise nx.NodeNotFound( + "The node(s) " + str(list(C - V)) + " are not " "in the graph." + ) + V_C = V - C # set of nodes in V but not in C + # accumulation + for pair in combinations(V_C, 2): # (s, t) pairs of V_C + try: + paths = 0 + paths_through_C = 0 + for path in nx.all_shortest_paths( + G, source=pair[0], target=pair[1], weight=weight + ): + if set(path) & C: + paths_through_C += 1 + paths += 1 + betweenness += paths_through_C / paths + except nx.exception.NetworkXNoPath: + betweenness += 0 + # rescaling + v, c = len(G), len(C) + if normalized: + scale = 1 / ((v - c) * (v - c - 1)) + if not G.is_directed(): + scale *= 2 + else: + scale = None + if scale is not None: + betweenness *= scale + return betweenness + + +def group_closeness_centrality(G, S, weight=None): + r"""Compute the group closeness centrality for a group of nodes. + + Group closeness centrality of a group of nodes $S$ is a measure + of how close the group is to the other nodes in the graph. + + .. math:: + + c_{close}(S) = \frac{|V-S|}{\sum_{v \in V-S} d_{S, v}} + + d_{S, v} = min_{u \in S} (d_{u, v}) + + where $V$ is the set of nodes, $d_{S, v}$ is the distance of + the group $S$ from $v$ defined as above. ($V-S$ is the set of nodes + in $V$ that are not in $S$). + + Parameters + ---------- + G : graph + A NetworkX graph. + + S : list or set + S is a group of nodes which belong to G, for which group closeness + centrality is to be calculated. + + weight : None or string, optional (default=None) + If None, all edge weights are considered equal. + Otherwise holds the name of the edge attribute used as weight. + + Raises + ------ + NodeNotFound + If node(s) in S are not present in G. + + Returns + ------- + closeness : float + Group closeness centrality of the group S. + + See Also + -------- + closeness_centrality + + Notes + ----- + The measure was introduced in [1]_. + The formula implemented here is described in [2]_. + + Higher values of closeness indicate greater centrality. + + It is assumed that 1 / 0 is 0 (required in the case of directed graphs, + or when a shortest path length is 0). + + The number of nodes in the group must be a maximum of n - 1 where `n` + is the total number of nodes in the graph. + + For directed graphs, the incoming distance is utilized here. To use the + outward distance, act on `G.reverse()`. + + For weighted graphs the edge weights must be greater than zero. + Zero edge weights can produce an infinite number of equal length + paths between pairs of nodes. + + References + ---------- + .. [1] M G Everett and S P Borgatti: + The Centrality of Groups and Classes. + Journal of Mathematical Sociology. 23(3): 181-201. 1999. + http://www.analytictech.com/borgatti/group_centrality.htm + .. [2] J. Zhao et. al.: + Measuring and Maximizing Group Closeness Centrality over + Disk Resident Graphs. + WWWConference Proceedings, 2014. 689-694. + http://wwwconference.org/proceedings/www2014/companion/p689.pdf + """ + if G.is_directed(): + G = G.reverse() # reverse view + closeness = 0 # initialize to 0 + V = set(G) # set of nodes in G + S = set(S) # set of nodes in group S + V_S = V - S # set of nodes in V but not S + shortest_path_lengths = nx.multi_source_dijkstra_path_length(G, S, weight=weight) + # accumulation + for v in V_S: + try: + closeness += shortest_path_lengths[v] + except KeyError: # no path exists + closeness += 0 + try: + closeness = len(V_S) / closeness + except ZeroDivisionError: # 1 / 0 assumed as 0 + closeness = 0 + return closeness + + +def group_degree_centrality(G, S): + """Compute the group degree centrality for a group of nodes. + + Group degree centrality of a group of nodes $S$ is the fraction + of non-group members connected to group members. + + Parameters + ---------- + G : graph + A NetworkX graph. + + S : list or set + S is a group of nodes which belong to G, for which group degree + centrality is to be calculated. + + Raises + ------ + NetworkXError + If node(s) in S are not in G. + + Returns + ------- + centrality : float + Group degree centrality of the group S. + + See Also + -------- + degree_centrality + group_in_degree_centrality + group_out_degree_centrality + + Notes + ----- + The measure was introduced in [1]_. + + The number of nodes in the group must be a maximum of n - 1 where `n` + is the total number of nodes in the graph. + + References + ---------- + .. [1] M G Everett and S P Borgatti: + The Centrality of Groups and Classes. + Journal of Mathematical Sociology. 23(3): 181-201. 1999. + http://www.analytictech.com/borgatti/group_centrality.htm + """ + centrality = len(set().union(*list(set(G.neighbors(i)) for i in S)) - set(S)) + centrality /= len(G.nodes()) - len(S) + return centrality + + +@not_implemented_for("undirected") +def group_in_degree_centrality(G, S): + """Compute the group in-degree centrality for a group of nodes. + + Group in-degree centrality of a group of nodes $S$ is the fraction + of non-group members connected to group members by incoming edges. + + Parameters + ---------- + G : graph + A NetworkX graph. + + S : list or set + S is a group of nodes which belong to G, for which group in-degree + centrality is to be calculated. + + Returns + ------- + centrality : float + Group in-degree centrality of the group S. + + Raises + ------ + NetworkXNotImplemented + If G is undirected. + + NodeNotFound + If node(s) in S are not in G. + + See Also + -------- + degree_centrality + group_degree_centrality + group_out_degree_centrality + + Notes + ----- + The number of nodes in the group must be a maximum of n - 1 where `n` + is the total number of nodes in the graph. + + `G.neighbors(i)` gives nodes with an outward edge from i, in a DiGraph, + so for group in-degree centrality, the reverse graph is used. + """ + return group_degree_centrality(G.reverse(), S) + + +@not_implemented_for("undirected") +def group_out_degree_centrality(G, S): + """Compute the group out-degree centrality for a group of nodes. + + Group out-degree centrality of a group of nodes $S$ is the fraction + of non-group members connected to group members by outgoing edges. + + Parameters + ---------- + G : graph + A NetworkX graph. + + S : list or set + S is a group of nodes which belong to G, for which group in-degree + centrality is to be calculated. + + Returns + ------- + centrality : float + Group out-degree centrality of the group S. + + Raises + ------ + NetworkXNotImplemented + If G is undirected. + + NodeNotFound + If node(s) in S are not in G. + + See Also + -------- + degree_centrality + group_degree_centrality + group_in_degree_centrality + + Notes + ----- + The number of nodes in the group must be a maximum of n - 1 where `n` + is the total number of nodes in the graph. + + `G.neighbors(i)` gives nodes with an outward edge from i, in a DiGraph, + so for group out-degree centrality, the graph itself is used. + """ + return group_degree_centrality(G, S)