google_matrix(G, alpha=0.85, personalization=None, nodelist=None, weight='weight', dangling=None)
The matrix returned represents the transition matrix that describes the Markov chain used in PageRank. For PageRank to converge to a unique solution (i.e., a unique stationary distribution in a Markov chain), the transition matrix must be irreducible. In other words, it must be that there exists a path between every pair of nodes in the graph, or else there is the potential of "rank sinks."
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.
A NetworkX graph. Undirected graphs will be converted to a directed graph with two directed edges for each undirected edge.
The damping factor.
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.
The rows and columns are ordered according to the nodes in nodelist. If nodelist is None, then the ordering is produced by G.nodes().
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 below). It may be common to have the dangling dict to be the same as the personalization dict.
Google matrix of the graph
Returns the Google matrix of the graph.
The following pages refer to to this document either explicitly or contain code examples using this.
networkx.algorithms.link_analysis.pagerank_alg.pagerank
networkx.algorithms.link_analysis.pagerank_alg.pagerank_numpy
networkx.algorithms.link_analysis.pagerank_alg.pagerank_scipy
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