U A·fw ã@sdZdgZddd„ZdS)z@Algorithm to select influential nodes in a graph using VoteRank.ÚvoterankNcsºg}i‰t|ƒdkr|S|dks,|t|ƒkr4t|ƒ}| ¡r\tdd„| ¡Dƒƒt|ƒ}ntdd„| ¡Dƒƒt|ƒ}| ¡D]}ddgˆ|<q‚t|ƒD]}| ¡D]}dˆ|d<qª| ¡D]H\}}ˆ|dˆ|d7<| ¡sĈ|dˆ|d7<qÄ|D]}dˆ|d<qt|j‡fdd„d }ˆ|ddkrV|S|  |¡ddgˆ|<| |¡D]<\}}ˆ|dd|8<tˆ|ddƒˆ|d<qvqœ|S) a´Select 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. éNcss|]\}}|VqdS©N©©Ú.0Ú_ÚdegrrúO/tmp/pip-unpacked-wheel-0wvcsx6h/networkx/algorithms/centrality/voterank_alg.pyÚ =szvoterank..css|]\}}|VqdSrrrrrr r @sécs ˆ|dS)Nrr)Úx©Z vote_rankrr ÚRózvoterank..)Úkey) ÚlenZ is_directedÚsumZ out_degreeZdegreeZnodesÚrangeÚedgesÚmaxÚappend)ÚGZnumber_of_nodesZinfluential_nodesZ avgDegreeÚnrZnbrrr r rs:/       )N)Ú__doc__Ú__all__rrrrr Ús