EdgeCycleMatrix

EdgeCycleMatrix[g]
gives the edge cycle matrix of a graph g.

DetailsDetails

  • EdgeCycleMatrix is also known as tie-set matrix or loop matrix.
  • EdgeCycleMatrix returns a matrix where each row corresponds to a cycle i in the graph g, and each column corresponds to an edge .
  • For an undirected graph, is if edge is part of cycle i and zero otherwise.
  • For a directed graph, is if edge is part of cycle i, if edge in reverse direction is part of cycle i, and zero otherwise.
  • Edge is the edge as position j in EdgeList[g], and the index j for an edge can be found from EdgeIndex[g,ej].
  • EdgeCycleMatrix gives a basis for all the cycles in the graph g.
  • EdgeCycleMatrix works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

Background
Background

  • EdgeCycleMatrix returns a matrix in which each row corresponds to a cycle i in a graph and each column corresponds to an edge . An edge cycle matrix is determined by the incidences of edges and cycles in a graph, and cycles in a edge cycle matrix form a cycle basis of a graph. Cycle bases are useful to study chemical graphs, to generate a large cycle families, and to compute voltage or current in a circuit. Edge cycle matrices are also known as tie-set or loop matrices.
  • For an undirected graph, is if edge is part of cycle i and zero otherwise. For a directed graph, is if edge is part of cycle i, if edge in reverse direction is part of cycle i, and zero otherwise.
  • FindFundamentalCycles is a related function that can be used to return a list of fundamental cycles of a graph.
Introduced in 2014
(10.0)