# Strongly Connected Components in Stream Graphs: Computation and Experimentations

Abstract : Stream graphs model highly dynamic networks in which nodes and/or links arrive and/or leave over time. Strongly connected components in stream graphs were defined recently, but no algorithm was provided to compute them. We present here several solutions with polynomial time and space complexities, each with its own strengths and weaknesses. We provide an implementation and experimentally compare the algorithms in a wide variety of practical cases. In addition, we propose an approximation scheme that significantly reduces computation costs, and gives even more insight on the dataset. Connected components are among the most important concepts of graph theory. They were recently generalized to stream graphs [18], a formal object that captures the dynamics of nodes and links over time. Unlike other generalizations available in the literature, these generalized connected components partition the set of temporal nodes. This means that each node at each time instant is in one and only one connected component. This makes these generalized connected components particularly appealing to capture important features of objects modeled by stream graphs. However, computation of connected components in stream graphs has not been explored yet. Therefore, up to this date, they remain a formal object with no practical use. In addition, the algorithmic complexity of the problem is unknown, as well as the insight they may shed on real-world stream graphs of interest. After introducing key notations and definitions (Section 1), we present two algorithms for strongly connected components, together with their complexity (Section 2). We then apply these algorithms to several large-scale real-world datasets and demonstrate their ability to describe such datasets (Section 3). We also show that their performances may be improved greatly at the cost of reasonable approximations. 1 The Stream Graph Framework Given any two sets A and B, we denote by A ⊗ B the set of pairs ab such that a ∈ A, b ∈ B and a = b. Couples are ordered, while pairs are unordered: (a, b) = (b, a) while ab = ba.
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https://hal.archives-ouvertes.fr/hal-02999870
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Submitted on : Wednesday, November 11, 2020 - 10:59:23 AM
Last modification on : Tuesday, March 23, 2021 - 9:28:02 AM
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• HAL Id : hal-02999870, version 1

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Léo Rannou, Clémence Magnien, Matthieu Latapy. Strongly Connected Components in Stream Graphs: Computation and Experimentations. The 9th International Conference on Complex Networks and their Applications (Complex Networks 2020), 2020, Madrid (virtual), Spain. ⟨hal-02999870⟩