An algebraic approach to temporal network analysis based on temporal quantities

TL;DR

This paper introduces an algebraic framework using temporal quantities and semirings for direct analysis of temporal networks, enabling efficient computation of dynamic network characteristics without slicing.

Contribution

It presents a novel algebraic approach with algorithms and software for analyzing temporal networks directly through temporal quantities, improving over traditional slicing methods.

Findings

Implemented fast algorithms for temporal network operations

Applied methods to violence and terror news networks

Enabled direct computation of network characteristics

Abstract

In a temporal network, the presence and activity of nodes and links can change through time. To describe temporal networks we introduce the notion of temporal quantities. We define the addition and multiplication of temporal quantities in a way that can be used for the definition of addition and multiplication of temporal networks. The corresponding algebraic structures are semirings. The usual approach to (data) analysis of temporal networks is to transform it into a sequence of time slices -- static networks corresponding to selected time intervals and analyze each of them using standard methods to produce a sequence of results. The approach proposed in this paper enables us to compute these results directly. We developed fast algorithms for the proposed operations. They are available as an open source Python library TQ (Temporal Quantities) and a program Ianus. The proposed approach enables us to treat as temporal quantities also other network characteristics such as degrees, connectivity components, centrality measures, Pathfinder skeleton, etc. To illustrate the developed tools we present some results from the analysis of Franzosi's violence network and Corman's Reuters terror news network.