networkx.pagerank

pagerank(G, alpha=0.84999999999999998, max_iter=100, tol=1e-08, nstart=None)

Return the PageRank of the nodes in the graph.

PageRank computes the largest eigenvector of the stochastic adjacency matrix of G.

Parameters:

G : graph

A networkx graph

alpha : float, optional

Parameter for PageRank, default=0.85

max_iter : interger, optional

Maximum number of iterations in power method.

tol : float, optional

Error tolerance used to check convergence in power method iteration.

nstart : dictionary, optional

Starting value of PageRank iteration for each node.

Returns:

nodes : dictionary

Dictionary of nodes with value as PageRank

Notes

The eigenvector calculation is done by the power iteration method and has no guarantee of convergence. The iteration will stop after max_iter iterations or an error tolerance of number_of_nodes(G)*tol has been reached.

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.

For an overview see: A. Langville and C. Meyer, “A survey of eigenvector methods of web information retrieval.” http://citeseer.ist.psu.edu/713792.html

Examples

>>> G=nx.DiGraph(nx.path_graph(4))
>>> pr=nx.pagerank(G,alpha=0.9)