Year: 2022
Type: preprint
Abstract: The $k$-th power of the adjacency matrix of a simple undirected graph represents the number of walks with length $k$ between pairs of nodes. As a walk where no node repeats, a path is a walk where each node is only visited once. The set of paths constitutes a relatively small subset of all possible walks. We introduce three types of walks, representing subsets of all possible walks. Considered types of walks allow for deriving an analytic solution for the number of paths of a certain length between node pairs in a matrix form. Depending on the path length, different approaches possess the lowest computational complexity. We also propose a recursive algorithm for determining all paths in a graph, which can be generalised to directed (un)weighted networks.
Source: arXiv (Cornell University)
Authors: Jokić, Ivan, Van Mieghem, Piet
Institution: Delft University of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4296567738