An integrative dynamical perspective for graph theory and the study of complex networks

TL;DR

This paper challenges the universality of classical graph theory for complex networks, proposing a model-based perspective that links graph metrics to propagation dynamics, enabling tailored analyses for different network types.

Contribution

It introduces a model-based framework connecting graph metrics to propagation models, allowing customized and interpretable network analyses based on underlying dynamics.

Findings

Classical graph metrics derive from a hidden propagation model.

Network topology and dynamics should be studied jointly.

The framework enables designing tailored network analysis methods.

Abstract

Built upon the shoulders of graph theory, the field of complex networks has become a central tool for studying real systems across various fields of research. Represented as graphs, different systems can be studied using the same analysis methods, which allows for their comparison. Here, we challenge the wide-spread idea that graph theory is a universal analysis tool, uniformly applicable to any kind of network data. Instead, we show that many classical graph metrics (including degree, clustering coefficient and geodesic distance) arise from a common hidden propagation model: the discrete cascade. From this perspective, graph metrics are no longer regarded as combinatorial measures of the graph, but as spatio-temporal properties of the network dynamics unfolded at different temporal scales. Once graph theory is seen as a model-based (and not a purely data-driven) analysis tool, we can freely or intentionally replace the discrete cascade by other canonical propagation models and define new network metrics. This opens the opportunity to design, explicitly and transparently, dedicated analyses for different types of real networks by choosing a propagation model that matches their individual constraints. In this way, we take stand that network topology cannot always be abstracted independently from network dynamics, but shall be jointly studied. Which is key for the interpretability of the analyses. The model-based perspective here proposed serves to integrate into a common context both the classical graph analysis and the more recent network metrics defined in the literature which were, directly or indirectly, inspired by propagation phenomena on networks.