CyclePathCount(A,L0​)

Algorithm for counting simple paths & cycles of any length on any (weighted directed) network.

This is a Matlab implementation of the general purpose algorithm for counting simple cycles and simple paths presented in the article "A general purpose algorithm for counting simple cycles and simple paths of any length" available at https://arxiv.org/abs/1612.05531. Simple cycles, a.k.a elementary circuits, self-avoiding walks, are cycles that do not visit any vertex more than once. Simple paths, a.k.a self-avoiding walks, are open walks that do not visit any vertex more than once.
The algorithm, a combinatorial sieve, counts simple cycles (self-loops, backtracks, triangles, squares, pentagons, etc.) & simple paths of any length on both directed and undirected networks, returning a cell array, Primes, where Primes{i} is a matrix whose kl entry is the number of simple paths of length 1<=i<=L0 from vertex k to vertex l. Entry kk is the number of simple cycles of length 0<=i<=L0 from k to itself. The algorithm also works on weighted graphs, where it returns the sum of the weights of the simple paths/cycles of any given length.

Use as follows:
[Primes,elapsedTime] = CyclePathCount(A,L0)
with Primes the cell-array with the number of simple paths/cycles, A the graph adjacency matrix and L0 the maximum length up to which to count the simple paths/cycles.