D^(hdZddlZddlmZddlmZgdZedejdZ edejd Z edejd Z y) zDProvides functions for computing the efficiency of nodes and graphs.N)NetworkXNoPath)not_implemented_for) efficiencylocal_efficiencyglobal_efficiencydirectedc` dtj|||z }|S#t$rd}Y|SwxYw)adReturns 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. r)nxshortest_path_lengthr)Guveffs e/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/networkx/algorithms/efficiency_measures.pyrr sCX"))!Q22 J  Js  --ct|}||dz z}|dk7rNtj|}d}|D]+\}}|jD]\}}|dkDs |d|z z }-||z}|Sd}|S)a3Returns 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. r r)lenr all_pairs_shortest_path_lengthitems) rndenomlengthsg_effsourcetargetstargetdistances rrr>sT AA QKE z33A6& *OFG$+MMO * a<Q\)E * *  L LcHfdD}t|tz S)aReturns 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. c3XK|]!}tj|#yw)N)rsubgraph).0rrs r z#local_efficiency..s$Fq(AaD)9:Fs'*)sumr)refficiency_lists` rrr{s%VGAFO  #a& ((r) __doc__networkxr networkx.exceptionrutilsr__all__ _dispatchablerrrrrr.sJ-' AZ .!.bZ 8!8vZ *)!*)r