Related papers: Phase transitions on heterogeneous random graphs: …
Our general subject is the emergence of phases, and phase transitions, in large networks subjected to a few variable constraints. Our main result is the analysis, in the model using edge and triangle subdensities for constraints, of a sharp…
The quantitative study of traffic dynamics is crucial to ensure the efficiency of urban transportation networks. The current work investigates the spatial properties of congestion, that is, we aim to characterize the city areas where…
We introduce a very general model of an inhomogenous random graph with independence between the edges, which scales so that the number of edges is linear in the number of vertices. This scaling corresponds to the p=c/n scaling for G(n,p)…
Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations…
Group-based reinforcement can induce discontinuous transitions from inactive to active phases in higher-order contagion models. However, these results are typically obtained on static interaction structures or within mean-field…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive graphs and trees.
We investigate critical behaviors of a social contagion model on weighted networks. An edge-weight compartmental approach is applied to analyze the weighted social contagion on strongly heterogenous networks with skewed degree and weight…
The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their…
Due to their conceptual and mathematical simplicity, Erd\"os-R\'enyi or classical random graphs remain as a fundamental paradigm to model complex interacting systems in several areas. Although condensation phenomena have been widely…
Social fragmentation transition is a transition of social states between many disconnected communities with distinct opinions and a well-connected single network with homogeneous opinions. This is a timely research topic with high relevance…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
In this thesis we contribute to the understanding of the pivotal role of the temporal dimension in networked social systems, previously neglected and now uncovered by the data revolution recently blossomed in this field. To this aim, we…
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…
Although static networks have been extensively studied in machine learning, data mining, and AI communities for many decades, the study of dynamic networks has recently taken center stage due to the prominence of social media and its…
Phase transitions constitute fundamental mechanisms underlying abrupt or qualitative changes in the collective dynamics of interacting units across a wide range of natural and engineered systems. In dynamical networks, such transitions lead…
We study the behavior of solutions of mutually coupled equations in heterogeneous random graphs. Heterogeneity means that some equations receive many inputs whereas most of the equations are given only with a few connections. Starting from…
The interplay between time scales and structural properties of complex networks of nonlinear oscillators can generate many interesting phenomena, like amplitude death, cluster synchronization, frequency synchronization etc. We study the…