pagerank(G, alpha=0.85, personalization=None, max_iter=100, tol=1e-06, nstart=None, weight='weight', dangling=None)
PageRank computes a ranking of the nodes in the graph G based on the structure of the incoming links. It was originally designed as an algorithm to rank web pages.
The eigenvector calculation is done by the power iteration method and has no guarantee of convergence. The iteration will stop after an error tolerance of len(G) * tol
has been reached. If the number of iterations exceed :None:None:`max_iter`, a networkx.exception.PowerIterationFailedConvergence
exception is raised.
The PageRank algorithm was designed for directed graphs but this algorithm does not check if the input graph is directed and will execute on undirected graphs by converting each edge in the directed graph to two edges.
A NetworkX graph. Undirected graphs will be converted to a directed graph with two directed edges for each undirected edge.
Damping parameter for PageRank, default=0.85.
The "personalization vector" consisting of a dictionary with a key some subset of graph nodes and personalization value each of those. At least one personalization value must be non-zero. If not specfiied, a nodes personalization value will be zero. By default, a uniform distribution is used.
Maximum number of iterations in power method eigenvalue solver.
Error tolerance used to check convergence in power method solver.
Starting value of PageRank iteration for each node.
Edge data key to use as weight. If None weights are set to 1.
The outedges to be assigned to any "dangling" nodes, i.e., nodes without any outedges. The dict key is the node the outedge points to and the dict value is the weight of that outedge. By default, dangling nodes are given outedges according to the personalization vector (uniform if not specified). This must be selected to result in an irreducible transition matrix (see notes under google_matrix). It may be common to have the dangling dict to be the same as the personalization dict.
If the algorithm fails to converge to the specified tolerance within the specified number of iterations of the power iteration method.
Dictionary of nodes with PageRank as value
Returns the PageRank of the nodes in the graph.
>>> G = nx.DiGraph(nx.path_graph(4))See :
... pr = nx.pagerank(G, alpha=0.9)
The following pages refer to to this document either explicitly or contain code examples using this.
networkx.algorithms.centrality.eigenvector.eigenvector_centrality_numpy
networkx.algorithms.link_analysis.pagerank_alg.pagerank
networkx.algorithms.link_analysis.pagerank_alg.pagerank_scipy
networkx.algorithms.centrality.katz.katz_centrality
networkx.algorithms.centrality.eigenvector.eigenvector_centrality
networkx.algorithms.link_analysis.pagerank_alg.google_matrix
networkx.algorithms.centrality.katz.katz_centrality_numpy
networkx.algorithms.link_analysis.pagerank_alg.pagerank_numpy
Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them