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author | S. Solomon Darnell | 2025-03-28 21:52:21 -0500 |
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committer | S. Solomon Darnell | 2025-03-28 21:52:21 -0500 |
commit | 4a52a71956a8d46fcb7294ac71734504bb09bcc2 (patch) | |
tree | ee3dc5af3b6313e921cd920906356f5d4febc4ed /.venv/lib/python3.12/site-packages/networkx/algorithms/centrality/current_flow_closeness.py | |
parent | cc961e04ba734dd72309fb548a2f97d67d578813 (diff) | |
download | gn-ai-master.tar.gz |
Diffstat (limited to '.venv/lib/python3.12/site-packages/networkx/algorithms/centrality/current_flow_closeness.py')
-rw-r--r-- | .venv/lib/python3.12/site-packages/networkx/algorithms/centrality/current_flow_closeness.py | 96 |
1 files changed, 96 insertions, 0 deletions
diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/centrality/current_flow_closeness.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/centrality/current_flow_closeness.py new file mode 100644 index 00000000..67f86397 --- /dev/null +++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/centrality/current_flow_closeness.py @@ -0,0 +1,96 @@ +"""Current-flow closeness centrality measures.""" + +import networkx as nx +from networkx.algorithms.centrality.flow_matrix import ( + CGInverseLaplacian, + FullInverseLaplacian, + SuperLUInverseLaplacian, +) +from networkx.utils import not_implemented_for, reverse_cuthill_mckee_ordering + +__all__ = ["current_flow_closeness_centrality", "information_centrality"] + + +@not_implemented_for("directed") +@nx._dispatchable(edge_attrs="weight") +def current_flow_closeness_centrality(G, weight=None, dtype=float, solver="lu"): + """Compute current-flow closeness centrality for nodes. + + Current-flow closeness centrality is variant of closeness + centrality based on effective resistance between nodes in + a network. This metric is also known as information centrality. + + Parameters + ---------- + G : graph + A NetworkX graph. + + 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. + The weight reflects the capacity or the strength of the + edge. + + dtype: data type (default=float) + Default data type for internal matrices. + Set to np.float32 for lower memory consumption. + + solver: string (default='lu') + Type of linear solver to use for computing the flow matrix. + Options are "full" (uses most memory), "lu" (recommended), and + "cg" (uses least memory). + + Returns + ------- + nodes : dictionary + Dictionary of nodes with current flow closeness centrality as the value. + + See Also + -------- + closeness_centrality + + Notes + ----- + The algorithm is from Brandes [1]_. + + See also [2]_ for the original definition of information centrality. + + References + ---------- + .. [1] Ulrik Brandes and Daniel Fleischer, + Centrality Measures Based on Current Flow. + Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS '05). + LNCS 3404, pp. 533-544. Springer-Verlag, 2005. + https://doi.org/10.1007/978-3-540-31856-9_44 + + .. [2] Karen Stephenson and Marvin Zelen: + Rethinking centrality: Methods and examples. + Social Networks 11(1):1-37, 1989. + https://doi.org/10.1016/0378-8733(89)90016-6 + """ + if not nx.is_connected(G): + raise nx.NetworkXError("Graph not connected.") + solvername = { + "full": FullInverseLaplacian, + "lu": SuperLUInverseLaplacian, + "cg": CGInverseLaplacian, + } + N = G.number_of_nodes() + ordering = list(reverse_cuthill_mckee_ordering(G)) + # make a copy with integer labels according to rcm ordering + # this could be done without a copy if we really wanted to + H = nx.relabel_nodes(G, dict(zip(ordering, range(N)))) + betweenness = dict.fromkeys(H, 0.0) # b[n]=0 for n in H + N = H.number_of_nodes() + L = nx.laplacian_matrix(H, nodelist=range(N), weight=weight).asformat("csc") + L = L.astype(dtype) + C2 = solvername[solver](L, width=1, dtype=dtype) # initialize solver + for v in H: + col = C2.get_row(v) + for w in H: + betweenness[v] += col.item(v) - 2 * col.item(w) + betweenness[w] += col.item(v) + return {ordering[node]: 1 / value for node, value in betweenness.items()} + + +information_centrality = current_flow_closeness_centrality |