Number of Cycles in a Graph

Number of Cycles

The maximum number of independent cycles in a graph (u) is estimated through the number of nodes (v), links (e) and of sub-graphs (p). Trees and simple networks have a value of 0 since they have no cycles. The more complex a network is, the higher the value of u, so it can be used as an indicator of the level of development and complexity of a transport system. The matrix on the above figure shows that graph A has no cycles (u=0) while graphs C and D have two cycles respectively.