# An algebraic approach to temporal network analysis based on temporal quantities

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## 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 the network 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.

## Keywords

Temporal network Time slice Temporal quantity Semiring Algorithm Network measures Python library Violence Terror## Mathematics Subject Classification

91D30 16Y60 90B10 68R10 93C55## Notes

### Acknowledgments

This work was supported in part by the ARRS, Slovenia, research program P1-0294 and research projects J5-5537 and J1-5433, as well as by a grant within the EURO-CORES Programme EUROGIGA (project GReGAS) of the European Science Foundation. The paper is based on our talks presented at the 1st European Conference on Social Networks, Barcelona (UAB), July 1–4, 2014.

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