U ?hw @sdZdgZdddZdS)z@Algorithm to select influential nodes in a graph using VoteRank.voterankNcsg}it|dkr|S|dks,|t|kr4t|}|r\tdd|Dt|}ntdd|Dt|}|D]}ddg|<qt|D]}|D]}d|d<q|D]H\}}|d|d7<|sĈ|d|d7<q|D]}d|d<qt|jfddd }|ddkrV|S| |ddg|<||D]<\}}|dd|8<t|dd|d<qvq|S) aSelect a list of influential nodes in a graph using VoteRank algorithm VoteRank [1]_ computes a ranking of the nodes in a graph G based on a voting scheme. With VoteRank, all nodes vote for each of its in-neighbours and the node with the highest votes is elected iteratively. The voting ability of out-neighbors of elected nodes is decreased in subsequent turns. Parameters ---------- G : graph A NetworkX graph. number_of_nodes : integer, optional Number of ranked nodes to extract (default all nodes). Returns ------- voterank : list Ordered list of computed seeds. Only nodes with positive number of votes are returned. Examples -------- >>> G = nx.Graph([(0, 1), (0, 2), (0, 3), (1, 4)]) >>> nx.voterank(G) [0, 1] The algorithm can be used both for undirected and directed graphs. However, the directed version is different in two ways: (i) nodes only vote for their in-neighbors and (ii) only the voting ability of elected node and its out-neighbors are updated: >>> G = nx.DiGraph([(0, 1), (2, 1), (2, 3), (3, 4)]) >>> nx.voterank(G) [2, 3] Notes ----- Each edge is treated independently in case of multigraphs. References ---------- .. [1] Zhang, J.-X. et al. (2016). Identifying a set of influential spreaders in complex networks. Sci. Rep. 6, 27823; doi: 10.1038/srep27823. Ncss|]\}}|VqdSN.0_degrr]/var/www/html/venv/lib/python3.8/site-packages/networkx/algorithms/centrality/voterank_alg.py =szvoterank..css|]\}}|VqdSrrrrrr r @scs |dS)Nrr)xZ vote_rankrr Rzvoterank..)key) lenZ is_directedsumZ out_degreeZdegreeZnodesrangeedgesmaxappend)GZnumber_of_nodesZinfluential_nodesZ avgDegreenrZnbrrr r rs:/       )N)__doc____all__rrrrr s