Inferring pattern generators on networks

Piotr Nyczka (1) , Marc-Thorsten Hütt (1) , Annick Lesne (2, 3)

1 Jacobs University of Bremen
2 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
3 IGMM - Institut de Génétique Moléculaire de Montpellier

Given a pattern on a network, i.e. a subset of nodes, can we assess, whether they are randomly distributed on the network or have been generated in a systematic fashion following the network architecture? This question is at the core of network-based data analyses across a range of disciplines-from incidents of infection in social networks to sets of differentially expressed genes in biological networks. Here we introduce generic 'pattern generators' based on an Eden growth model. We assess the capacity of different pattern measures like connectivity, edge density or various average distances, to infer the parameters of the generator from the observed patterns. Some measures perform consistently better than others in inferring the underlying pattern generator, while the best performing measures depend on the global topology of the underlying network. Moreover, we show that pattern generator inference remains possible in case of limited visibility of the patterns.

Mots clés: Patterns; Network clusters; Teleportation random walks; Eden model; Parametric inference; Mutual information

Domaines: Mécanique statistique [cond-mat.stat-mech]

Piotr Nyczka, Marc-Thorsten Hütt, Annick Lesne. Inferring pattern generators on networks. Physica A: Statistical Mechanics and its Applications, 2021, 566, pp.125631. ⟨10.1016/j.physa.2020.125631⟩. ⟨hal-03081091⟩