networkx.algorithms.link_analysis.pagerank_alg.pagerank_numpy¶

pagerank_numpy(G, alpha=0.85, personalization=None, weight='weight', dangling=None)[source]¶

Returns the PageRank of the nodes in the graph.

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.

Parameters

G (graph) – A NetworkX graph. Undirected graphs will be converted to a directed graph with two directed edges for each undirected edge.
alpha (float, optional) – Damping parameter for PageRank, default=0.85.
personalization (dict, optional) – 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.
weight (key, optional) – Edge data key to use as weight. If None weights are set to 1.
dangling (dict, optional) – 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.

Returns

pagerank – Dictionary of nodes with PageRank as value.

Return type

dictionary

Examples

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

Notes

The eigenvector calculation uses NumPy’s interface to the LAPACK eigenvalue solvers. This will be the fastest and most accurate for small graphs.

This implementation works with Multi(Di)Graphs. For multigraphs the weight between two nodes is set to be the sum of all edge weights between those nodes.