Towards Classifying the Polynomial-Time Solvability of Temporal Betweenness Centrality

TL;DR

This paper investigates the conditions under which temporal betweenness centrality can be computed efficiently, extending the understanding from static to dynamic graphs and classifying the complexity based on different shortest path notions.

Contribution

It provides a classification framework for the polynomial-time computability of temporal betweenness centrality based on various shortest path concepts.

Findings

Identifies conditions for polynomial-time solvability

Classifies shortest path notions by computational complexity

Extends static graph results to temporal graphs

Abstract

In static graphs, the betweenness centrality of a graph vertex measures how many times this vertex is part of a shortest path between any two graph vertices. Betweenness centrality is efficiently computable and it is a fundamental tool in network science. Continuing and extending previous work, we study the efficient computability of betweenness centrality in temporal graphs (graphs with fixed vertex set but time-varying arc sets). Unlike in the static case, there are numerous natural notions of being a "shortest" temporal path (walk). Depending on which notion is used, it was already observed that the problem is #P-hard in some cases while polynomial-time solvable in others. In this conceptual work, we contribute towards classifying what a "shortest path (walk) concept" has to fulfill in order to gain polynomial-time computability of temporal betweenness centrality.