brainconn.centrality.pagerank_centrality

pagerank_centrality(A, d, falff=None)[source]

The PageRank centrality is a variant of eigenvector centrality. This function computes the PageRank centrality of each vertex in a graph.

Formally, PageRank is defined as the stationary distribution achieved by instantiating a Markov chain on a graph. The PageRank centrality of a given vertex, then, is proportional to the number of steps (or amount of time) spent at that vertex as a result of such a process.

The PageRank index gets modified by the addition of a damping factor, d. In terms of a Markov chain, the damping factor specifies the fraction of the time that a random walker will transition to one of its current state’s neighbors. The remaining fraction of the time the walker is restarted at a random vertex. A common value for the damping factor is d = 0.85.

Parameters:
  • A (NxN numpy.ndarray) – adjacency matrix
  • d (float) – damping factor (see description)
  • falff (Nx1 numpy.ndarray or None) – Initial page rank probability, non-negative values. Default value is None. If not specified, a naive bayesian prior is used.
Returns:

r – vectors of page rankings
Return type:

Nx1 numpy.ndarray

Notes

The algorithm will work well for smaller matrices (number of nodes around 1000 or less)