2021/01/02 by Harrison Hartle, Fragkiskos Papadopoulos, Dmitri Krioukov · 12 citations
Mathematics · Physics and Astronomy · Psychology · #Artificial intelligence #Complex Network Analysis Techniques #Computer science #Function (biology) #Hidden variable theory #Latent variable #Mathematics #Mental Health Research Topics #Network model #Node (physics) #Opinion Dynamics and Social Influence #Statistical physics #Theoretical computer science #Variable (mathematics) #physics.soc-ph
paper · pdf · doi:10.1103/physreve.103.052307
published in Physical review. E 103(5), 052307 (American Physical Society) · 27 pages, 9 figures, 1 table
arxiv created 2021/01/02 · openalex publication_date 2021/05/13 · arxiv updated 2021/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time and many exhibit dynamics of node characteristics as well as of linking structure. Here we introduce and study natural temporal extensions of static hidden-variable network models with stochastic dynamics of hidden variables and links. The dynamics is controlled by two parameters: one that tunes the rate of change of hidden variables and another that tunes the rate at which node pairs reevaluate their connections given the current values of hidden variables. Snapshots of networks in the dynamic models are equivalent to networks generated by the static models only if the link reevaluation rate is sufficiently larger than the rate of hidden-variable dynamics or if an additional mechanism is added whereby links actively respond to changes in hidden variables. Otherwise, links are out of equilibrium with respect to hidden variables and network snapshots exhibit structural deviations from the static models. We examine the level of structural persistence in the considered models and quantify deviations from staticlike behavior. We explore temporal versions of popular static models with community structure, latent geometry, and degree heterogeneity. While we do not attempt to directly model real networks, we comment on interesting qualitative resemblances to real systems. In particular, we speculate that links in some real networks are out of equilibrium with respect to hidden variables, partially explaining the presence of long-ranged links in geometrically embedded systems and intergroup connectivity in modular systems. We also discuss possible extensions, generalizations, and applications of the introduced class of dynamic network models.