MultiNet Webinar Series

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Two shorter talks: Directed Percolation in Temporal Networks (Karsai); A Variance-aware Multiobjective Louvain-like Method for Community Detection in Multiplex Networks (Venturini)

Márton Karsai and Sara Venturini

Central European University and University of Padova, Italy

(Karsai) Connectivity and reachability on temporal networks, which can describe the spreading of a disease, decimation of information or the accessibility of a public transport system over time, have been among the main contemporary areas of study in complex systems for the last decade. However, while isotropic percolation theory successfully describes connectivity in static networks, a similar description has not been yet developed for temporal networks. In this talk we will address this problem and formalize a mapping of the concept of temporal network reachability to percolation theory [1,2]. We will find that the limited-waiting-time reachability, a generic notion of constrained connectivity in temporal networks, displays directed percolation phase transition in connectivity. Consequently, the critical percolation properties of spreading processes on temporal networks can be estimated by a set of known exponents characterising the directed percolation universality class. This result is robust across a diverse set of temporal network models with different temporal and topological heterogeneities, while by using our methodology we uncover similar reachability phase transitions in real temporal networks too.

[1] Badie-Modiri, A., Rizi, A.K., Karsai, M. and Kivelä, M., 2022. Directed percolation in temporal networks. Physical Review Research, 4(2), p.L022047.

[2] Badie-Modiri, Arash, Abbas K. Rizi, Márton Karsai, and Mikko Kivelä. "Directed percolation in random temporal network models with heterogeneities." Physical Review E 105, no. 5 (2022): 054313.

(Venturini) We focus on the community detection problem in multiplex networks, i.e., networks with multiple layers having same node sets and no inter-layer connections. In particular, we look for groups of nodes that can be recognized as communities consistently across the layers. To this end, we propose a new approach that generalizes the Louvain method by (a) simultaneously updating average and variance of the modularity scores across the layers, and (b) reformulating the greedy search procedure in terms of a filter-based multiobjective optimization scheme. Unlike many previous modularity maximization strategies, which rely on some form of aggregation of the various layers, our multiobjective approach aims at maximizing the individual modularities on each layer simultaneously. We did experiments on synthetic and real-world networks, showing the effectiveness and the robustness of the proposed strategies both in the informative case, where all layers show the same community structure, and in the noisy case, where some layers represent only noise.

Márton Karsai is an Associate Professor at the Department of Network and Data Science at the Central European University in Vienna. He is a researcher at the Rényi Institute of Mathematics in Budapest, Fellow of the ISI Foundation in Torino, director of the Network Science PhD program at CEU, where he leads the Computational Human Dynamics team. He is a network scientist with research interest in human dynamics, computational social science, and data science, especially focusing on heterogeneous temporal dynamics, spatial and temporal networks, socioeconomic systems and social contagion phenomena. He is an expert in analysing large human behavioural datasets and in developing data-driven models of social phenomena.

Sara Venturini is a PhD student of Computational Mathematics at the University of Padova, Italy. She obtained her Bachelor and Master Degree in Mathematics at the University of Padova. Her research interests include complex networks and optimization. She is working both on the computational analysis of complex networks and their applications to the real world. In particular, she has worked on multiplex, community detection and the Science of Science.


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