Related papers: First-passage phenomena in hierarchical networks
High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…
This article formalizes the problem of modeling social networks into an interacting particle system on random geometric graphs. Each vertex of the graph is associated with a geometric position in a latent space describing the unobserved…
General upper bounds on fluctuations of trajectory observables were recently obtained. It turned out that the size of fluctuations of dynamical observable is limited from below and from above. For the moment generating function of general…
We study the structural constraint of random scale-free networks that determines possible combinations of the degree exponent $\gamma$ and the upper cutoff $k_c$ in the thermodynamic limit. We employ the framework of graphicality…
We consider random walks evolving on two models of connected and undirected graphs and study the exact large deviations of a local dynamical observable. We prove, in the thermodynamic limit, that this observable undergoes a first-order…
Networks are essential models in many applications such as information technology, chemistry, power systems, transportation, neuroscience, and social sciences. In light of such broad applicability, a general theory of dynamical systems on…
In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths…
The spread of an infectious disease can, in some cases, promote the propagation of other pathogens favouring violent outbreaks, which cause a discontinuous transition to an endemic state. The topology of the contact network plays a crucial…
The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability…
Practical wireless networks are finite, and hence non-stationary with nodes typically non-homo-geneously deployed over the area. This leads to a location-dependent performance and to boundary effects which are both often neglected in…
We investigate local-density dependent Markov processes on a class of large graphs sampled from a graphon, where the transition rates of the vertices are influenced by the states of their neighbors. We show that as the average degree…
Many interdependent, real-world infrastructures involve interconnections between different communities or cities. Here we study if and how the effects of such interconnections can be described as an external field for interdependent…
We consider first passage percolation on the Erd\H{o}s--R\'{e}nyi graph with $n$ vertices in which each pair of distinct vertices is connected independently by an edge with probability $\lambda/n$ for some $\lambda>1$. The edges of the…
Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second-order Markov models, and derive an…
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…
We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…
For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random…
Topology of urban environments can be represented by means of graphs. We explore the graph representations of several compact urban patterns by random walks. The expected time of recurrence and the expected first passage time to a node…
The spectral properties of traditional (dyadic) graphs, where an edge connects exactly two vertices, are widely studied in different applications. These spectral properties are closely connected to the structural properties of dyadic…
Network properties govern the rate and extent of various spreading processes, from simple contagions to complex cascades. Recently, the analysis of spreading processes has been extended from static networks to temporal networks, where nodes…