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A significant generalization of the Erd\"os-R\'enyi random graph model is an `inhomogeneous' random graph where the edge probabilities vary according to vertex types. We identify the threshold value for this random graph with a finite…
The design of an efficient curing policy, able to stem an epidemic process at an affordable cost, has to account for the structure of the population contact network supporting the contagious process. Thus, we tackle the problem of…
We investigate the expected time to extinction in the susceptible-infectious-susceptible (SIS) model of disease spreading. Rather than using stochastic simulations, or asymptotic calculations in network models, we solve the extinction time…
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…
We consider bond percolation on random graphs with given degrees and bounded average degree. In particular, we consider the order of the largest component after the random deletion of the edges of such a random graph. We give a rough…
Infectious pathogens often propagate by superspreading, which focusses onward transmission on disproportionately few infected individuals. At the same time, infector-infectee pairs tend to have more similar transmission potentials than…
We introduce a probabilistic framework that represents stylized banking networks with the aim of predicting the size of contagion events. Most previous work on random financial networks assumes independent connections between banks, whereas…
Modeling of intricate relational patterns has become a cornerstone of contemporary statistical research and related data science fields. Networks, represented as graphs, offer a natural framework for this analysis. This paper extends the…
We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by…
Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible-infected-susceptible setting, spectral conditions characterise whether the disease vanishes. However, modelling human…
Non-uniform hypergraphs appear in various domains of computer science as in the satisfiability problems and in data analysis. We analyse a general model where the probability for an edge of size $t$ to belong to the hypergraph depends of a…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
Many real networks are not isolated from each other but form networks of networks, often interrelated in non trivial ways. Here, we analyze an epidemic spreading process taking place on top of two interconnected complex networks. We develop…
We study a random graph model in continuous time. Each vertex is partially copied with the same rate, i.e.\ an existing vertex is copied and every edge leading to the copied vertex is copied with independent probability $p$. In addition,…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
The number of triangles in a graph is useful to deduce a plethora of important features of the network that the graph is modeling. However, finding the exact value of this number is computationally expensive. Hence, a number of…
A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…
A random graph evolution based on the interactions of N vertices is studied. During the evolution both the preferential attachment method and the uniform choice of vertices are allowed. The weight of a vertex means the number of its…
We study the asymptotic growth rate of the label size of high-degree vertices in weighted recursive graphs (WRG) when the weights are i.i.d. almost surely bounded random variables, and as a result confirm a conjecture by Lodewijks and…