Thesis title: Multi-Scale Analysis of Structural and Dynamical Properties in Complex Networks
This thesis presents the research conducted during my PhD, focusing on the application of statistical mechanics to complex networks. By combining insights from statistical physics and graph theory, this work aims to enhance our understanding of the structural and dynamical properties of heterogeneous networks.
The first major contribution involves a novel framework for community detection using the Laplacian Renormalization Group method. This approach effectively reveals the modular structures within complex networks, demonstrating how networks optimize information exchange at various scales.
The second contribution investigates scale invariance, challenging the conventional association between scale-free networks and self-similarity, by defining a constant rate of entropy loss as a criterion for scale invariance.
The third part extends the Fluctuation-Dissipation Theorem to heterogeneous networks, introducing a dynamical centrality measure that accounts for variations in node importance over time. This method reveals how critical nodes adapt their influence based on diffusive processes, offering insights into the evolution of network structures.
Additionally, a parallel research explores a modified Wilson-Cowan model for neuronal populations, emphasizing the effects of non-normal coupling on neural dynamics. This work illustrates how these interactions influence bifurcations, reactivity, and synchronization.