Abstract
We discuss the temporal motifs approach that is aimed at detecting significant, intrinsically dynamic, mesoscopic structures and patterns in temporal networks, which cannot be seen in static or aggregated networks. Such patterns involve several nodes and their timed contacts. The approach consists of three phases: (1) identifying temporal subgraphs, (2) assigning the subgraphs to equivalence classes, and (3) assessing the relevance, surprise and significance of class-wise counts against some reference. We discuss these phases in detail, and apply the presented method to a temporal network of mobile telephone calls.
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Notes
- 1.
The configuration model is a random network with the same degree sequence as the empirical network.
- 2.
A graph G = (V, L) is connected iff there is a path between any two nodes, or equivalently when | L | ≥ 2, iff there is a path between any two edges. A subgraph G′ ⊆ G is induced if all nodes v i , v j ∈ G′ that are adjacent in G are also adjacent in G′.
- 3.
Two graphs G 1 and G 2 are isomorphic if there is a bijection σ : V 1 → V 2 of node labels such that σ(L 1) = L 2.
- 4.
Multigraphs are graphs where multiple edges between vertices are allowed.
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- 6.
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Acknowledgements
The authors acknowledge financial support by the EU 7th Framework Program’s FET-Open to ICTeCollective, project no. 238597, and support by the Academy of Finland to the project “Temporal networks of human interactions”, no. 260427. Lauri Kovanen is also supported by the doctoral program Brain & Mind.
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Kovanen, L., Karsai, M., Kaski, K., Kertész, J., Saramäki, J. (2013). Temporal Motifs. In: Holme, P., Saramäki, J. (eds) Temporal Networks. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36461-7_6
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