Expand an adjacency matrix to include higher-order neighborhoods

The node neighborhoods are expanded by multiplying the adjacency matrix k times. To make sure that all neighbors up to k steps away are included, self-loops are added by setting the diagonal of A to 1. These self-loops are removed from the resulting matrix after expansion. Note that the self-loops affect how the transition probabilities are calculated. When use_weights = FALSE, the edge values of the result from the matrix multiplication corresponds to the number of k-step random walks between any pair of nodes. For the expanded adjacency matrix, we replace these edge values with 1 so that the adjacency matrix corresponds to an unweighted graph with expanded neighborhoods.

Usage

expand_adjacency_matrix(A, k = 1L, use_weights = FALSE)

Arguments

A

An adjacency matrix. Can be a sparse matrix (dgCMatrix)

k

An integer specifying the neighborhood size. Each node will be connected to nodes up to k steps away.

use_weights

If TRUE, the transpose of the stochastic matrix will be expanded. The resulting edge weights will correspond to the incoming transition probabilities for a k-step random walk.

Value

An expanded adjacency matrix