The average disorder number of a simple connected graph on 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 (Fried 2022).

The average disorder number is related to the Wiener index of a graph with vertex count by

(Fried 2022).

More things to try:

Weisstein, Eric W. "Average Disorder Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AverageDisorderNumber.html