The average disorder number of a simple connected graph on n vertices is defined as the average length of a walk along the edges of the graph taken over all ordering of its vertices from 1 to n. The average disorder number A(G) is related to the Wiener index W(G) of a graph G with vertex count left bracketing bar G right bracketing bar by A(G) = (2W(G))/( left bracketing bar G right bracketing bar ) (Fried 2022).

disorder number | walk | Wiener index