Abstract
We recently introduced a formalism for the modeling of temporal networks, that we call stream graphs. It emphasizes the streaming nature of data and allows rigorous definitions of many important concepts generalizing classical graphs. This includes in particular size, density, clique, neighborhood, degree, clustering coefficient, and transitivity. In this contribution, we show that, like graphs, stream graphs may be extended to cope with bipartite structures, with node and link weights, or with link directions. We review the main bipartite, weighted or directed graph concepts proposed in the literature, we generalize them to the cases of bipartite, weighted, or directed stream graphs, and we show that obtained concepts are consistent with graph and stream graph ones. This provides a formal ground for an accurate modeling of the many temporal networks that have one or several of these features.
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Notes
- 1.
Given any two sets X and Y, we denote by \(X\times Y\) the cartesian product of X and Y, i.e. the set of all ordered pairs (x, y) such that \(x \in X\) and \(y \in Y\). We denote by \(X \otimes Y\) the set of all unordered pairs composed of \(x\in X\) and \(y\in Y\), with \(x\ne y\), that we denote by \(xy=yx\).
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Acknowledgements
This work is funded in part by the European Commission H2020 FETPROACT 2016–2017 program under grant 732942 (ODYCCEUS), by the ANR (French National Agency of Research) under grants ANR-15-CE38-0001 (AlgoDiv), by the Ile-de-France Region and its program FUI21 under grant 16010629 (iTRAC).
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Latapy, M., Magnien, C., Viard, T. (2023). Weighted, Bipartite, or Directed Stream Graphs for the Modeling of Temporal Networks. In: Holme, P., Saramäki, J. (eds) Temporal Network Theory. Computational Social Sciences. Springer, Cham. https://doi.org/10.1007/978-3-031-30399-9_3
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