U 9v fˆã@sbdZddlZddlmZddlmZdddgZed ƒd d„ƒZed ƒd d„ƒZ ed ƒd d„ƒZ dS) zDProvides functions for computing the efficiency of nodes and graphs.éN)ÚNetworkXNoPathé)Únot_implemented_forÚ efficiencyÚlocal_efficiencyÚglobal_efficiencyZdirectedcCs4zdt |||¡}Wntk r.d}YnX|S)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. ér)ÚnxZshortest_path_lengthr)ÚGÚuÚvZeff©r úK/tmp/pip-unpacked-wheel-_lngutwb/networkx/algorithms/efficiency_measures.pyr s + c Cspt|ƒ}||d}|dkrht |¡}d}|D].\}}| ¡D]\}}|dkr>|d|7}q>q.||}nd}|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. rr)Úlenr Zall_pairs_shortest_path_lengthÚitems) r ÚnZdenomÚlengthsZg_effÚsourceÚtargetsÚtargetZdistancer r rr=s)    cs"‡fdd„ˆDƒ}t|ƒtˆƒS)a¬Returns 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. c3s |]}tˆ ˆ|¡ƒVqdS)N)rZsubgraph)Ú.0r ©r r rÚ ¤sz#local_efficiency..)Úsumr)r Zefficiency_listr rrrys+) Ú__doc__Znetworkxr Znetworkx.exceptionrÚutilsrÚ__all__rrrr r r rÚs    1 ;