o ]ZŽh' ã@sjdZddlZddlmZddlmZddgZedd ƒejdd d„ƒƒZd d „Z edd ƒejd d„ƒƒZ dS)z8Algorithms to calculate reciprocity in a directed graph.éN)Ú NetworkXErroré)Únot_implemented_forÚ reciprocityÚoverall_reciprocityZ undirectedZ multigraphcCsL|durt|ƒS||vrtt||ƒƒd}|durtdƒ‚|Stt||ƒƒS)afCompute the reciprocity in a directed graph. The reciprocity of a directed graph is defined as the ratio of the number of edges pointing in both directions to the total number of edges in the graph. Formally, $r = |{(u,v) \in G|(v,u) \in G}| / |{(u,v) \in G}|$. The reciprocity of a single node u is defined similarly, it is the ratio of the number of edges in both directions to the total number of edges attached to node u. Parameters ---------- G : graph A networkx directed graph nodes : container of nodes, optional (default=whole graph) Compute reciprocity for nodes in this container. Returns ------- out : dictionary Reciprocity keyed by node label. Notes ----- The reciprocity is not defined for isolated nodes. In such cases this function will return None. NézNot defined for isolated nodes.)rÚnextÚ_reciprocity_iterrÚdict)ÚGÚnodesr©r úN/var/www/auris/lib/python3.10/site-packages/networkx/algorithms/reciprocity.pyr s!c cs|| |¡}|D]3}t| |¡ƒ}t| |¡ƒ}||@}t|ƒt|ƒ}|dkr.|dfVqdt|ƒ|}||fVqdS)z*Return an iterator of (node, reciprocity).rNr)Z nbunch_iterÚsetZ predecessorsÚ successorsÚlen) r r ÚnÚnodeÚpredÚsuccÚoverlapZn_totalrr r rr =s€   ôr cCs4| ¡}|| ¡ ¡d}|dkrtdƒ‚||S)z«Compute the reciprocity for the whole graph. See the doc of reciprocity for the definition. Parameters ---------- G : graph A networkx graph rrzNot defined for empty graphs)Znumber_of_edgesZ to_undirectedr)r Z n_all_edgeZn_overlap_edger r rrOs  )N) Ú__doc__ZnetworkxÚnxrÚutilsrÚ__all__Z _dispatchablerr rr r r rÚs  0