Dynamic Hidden-Variable Network Models

TL;DR

This paper introduces dynamic extensions to static hidden-variable network models, incorporating stochastic evolution of node properties and links, and analyzes how these dynamics affect network structure and persistence over time.

Contribution

It presents a novel framework for temporal hidden-variable network models with controllable dynamics, extending static models to include stochastic evolution of nodes and links.

Findings

Dynamic models can replicate static network properties under certain parameters.

The phase diagram characterizes regimes of static-like and dynamic behavior.

Structural persistence varies with the rates of hidden variable and link dynamics.

Abstract

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 rates of the hidden variable dynamics and link dynamics are controlled by two parameters, and snapshots of networks in the dynamic models may or may not be equivalent to a static model, depending on the location in the parameter phase diagram. We quantify deviations from static-like behavior, and examine the level of structural persistence in the considered models. We explore temporal versions of popular static models with community structure, latent geometry, and degree-heterogeneity. We do not attempt to directly model real networks, but comment on interesting qualitative resemblances, discussing possible extensions, generalizations, and applications.