Cycle Spaces of Digraphs

Chris Godsil, Krystal Guo

Published 2016-09-28Version 1

The cycle space of a graph corresponds to the kernel of an incidence matrix. We investigate an analogous subspace for digraphs. In the case of digraphs of graphs, where every edge is replaced by two oppositely directed arcs, we give a combinatorial description of a basis of such a space. We are motivated by a connection to the transition matrices of discrete-time quantum walks.