An integrative dynamical perspective for graph theory and the study of complex networks
arXiv (Cornell University)(2023)
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.
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Key words
graph theory,integrative dynamical perspective,networks,complex
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