Semirings for temporal network analysis

TL;DR

This paper introduces a novel algebraic framework using semirings for analyzing temporal networks, enabling computation of key metrics like foremost journeys and temporal betweenness centrality.

Contribution

It develops new semiring-based methods for temporal network analysis, including generalized centrality measures considering arbitrary waiting times and known link information.

Findings

Defined semiring for foremost journey computation

Introduced traveling semirings for complex temporal analysis

Calculated generalized temporal betweenness centrality

Abstract

In the article, we describe a new algebraic approach to the temporal network analysis based on the notion of temporal quantities. We define the semiring for computing the foremost journey and the traveling semirings for the analysis of temporal networks where the latency is given, the waiting times are arbitrary, and some other information on the links are known. We use the operations in the traveling semiring to compute a generalized temporal betweenness centrality of the nodes that corresponds to the importance of the nodes with respect to the ubiquitous foremost journeys in a temporal network.