A New Notion of Effective Resistance for Directed Graphs-Part II: Computing Resistances

TL;DR

This paper develops methods to compute effective resistance in directed graphs, revealing both familiar and unexpected behaviors compared to undirected cases, thereby advancing understanding of network robustness.

Contribution

It introduces computational techniques for effective resistance in directed graphs based on the theoretical framework from Part I, highlighting practical cases and behaviors.

Findings

Effective resistance can be computed for certain directed graphs.

The behavior of resistance in directed graphs can mirror or differ from undirected cases.

Some directed graphs exhibit unexpected resistance properties.

Abstract

In Part I of this work we defined a generalization of the concept of effective resistance to directed graphs, and we explored some of the properties of this new definition. Here, we use the theory developed in Part I to compute effective resistances in some prototypical directed graphs. This exploration highlights cases where our notion of effective resistance for directed graphs behaves analogously to our experience from undirected graphs, as well as cases where it behaves in unexpected ways.