+ )iRt^RIt^RIHt^RIHt.ROt]!R4]PR44t ]!R4]PR44t ]!R4]PR44t R#) zDProvides functions for computing the efficiency of nodes and graphs.N)NetworkXNoPath)not_implemented_fordirectedcl^\P!WV4, pV# \d^pT#i;i)aReturns the efficiency of a pair of nodes in a graph. The *efficiency* of a pair of nodes is the multiplicative inverse of the shortest path distance between the nodes [1]_. Returns 0 if no path between nodes. Parameters ---------- G : :class:`networkx.Graph` An undirected graph for which to compute the average local efficiency. u, v : node Nodes in the graph ``G``. Returns ------- float Multiplicative inverse of the shortest path distance between the nodes. Examples -------- >>> G = nx.Graph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)]) >>> nx.efficiency(G, 2, 3) # this gives efficiency for node 2 and 3 0.5 Notes ----- Edge weights are ignored when computing the shortest path distances. See also -------- local_efficiency global_efficiency References ---------- .. [1] Latora, Vito, and Massimo Marchiori. "Efficient behavior of small-world networks." *Physical Review Letters* 87.19 (2001): 198701. )nxshortest_path_lengthr)Guveffs&&& e/var/www/html/photoedit/myenv/lib/python3.14/site-packages/networkx/algorithms/efficiency_measures.py efficiencyr sAX"))!22 J  Js " 33c \V4pW^, ,pV^8wd`\P!V4p^pVF7wrVVP4FwrxV^8gKV^V, , pK K9 WB,pV#^pV#)aReturns the average global efficiency of the graph. The *efficiency* of a pair of nodes in a graph is the multiplicative inverse of the shortest path distance between the nodes. The *average global efficiency* of a graph is the average efficiency of all pairs of nodes [1]_. Parameters ---------- G : :class:`networkx.Graph` An undirected graph for which to compute the average global efficiency. Returns ------- float The average global efficiency of the graph. Examples -------- >>> G = nx.Graph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)]) >>> round(nx.global_efficiency(G), 12) 0.916666666667 Notes ----- Edge weights are ignored when computing the shortest path distances. See also -------- local_efficiency References ---------- .. [1] Latora, Vito, and Massimo Marchiori. "Efficient behavior of small-world networks." *Physical Review Letters* 87.19 (2001): 198701. )lenrall_pairs_shortest_path_lengthitems) rndenomlengthsg_effsourcetargetstargetdistances & r global_efficiencyr>sT AA QKE z33A6&OF$+MMO a<Q\)E%4 '  L LcRaV3RlS4p\V4\S4, #)a0Returns the average local efficiency of the graph. The *efficiency* of a pair of nodes in a graph is the multiplicative inverse of the shortest path distance between the nodes. The *local efficiency* of a node in the graph is the average global efficiency of the subgraph induced by the neighbors of the node. The *average local efficiency* is the average of the local efficiencies of each node [1]_. Parameters ---------- G : :class:`networkx.Graph` An undirected graph for which to compute the average local efficiency. Returns ------- float The average local efficiency of the graph. Examples -------- >>> G = nx.Graph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)]) >>> nx.local_efficiency(G) 0.9166666666666667 Notes ----- Edge weights are ignored when computing the shortest path distances. See also -------- global_efficiency References ---------- .. [1] Latora, Vito, and Massimo Marchiori. "Efficient behavior of small-world networks." *Physical Review Letters* 87.19 (2001): 198701. c3f<"TF&p\SPSV,44xK( R#5i)N)rsubgraph).0r rs& r #local_efficiency..s'FAq(AaD)9::As.1)sumr)refficiency_listsf r local_efficiencyr${s%VGAFO  #a& ((r)r r$r) __doc__networkxrnetworkx.exceptionrutilsr__all__ _dispatchabler rr$rr r,sJ-' AZ .!.bZ 8!8vZ *)!*)r