Expand an adjacency matrix to include higher-order neighborhoods
expand_adjacency_matrix.RdThe 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.
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
ksteps 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 ak-step random walk.- min_weight
A numeric value between 0 and 1 specifying the minimum weight threshold for edges in the expanded adjacency matrix. Only applicable when
use_weights = TRUE. Edges with weights below this threshold will be set to zero, effectively removing them from the graph. This can help to reduce noise and focus on stronger connections in the expanded neighborhood.