Related papers: Dynamics of hot random hyperbolic graphs
The object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynomial decay in the distance between them. Various aspects of…
We present a detailed study of the phase diagram of the Ising model in random graphs with arbitrary degree distribution. By using the replica method we compute exactly the value of the critical temperature and the associated critical…
In this paper we study a version of (non-Markovian) first passage percolation on graphs, where the transmission time between two connected vertices is non-iid, but increases by a penalty factor polynomial in their expected degrees. Based on…
The burning and forcing processes are both instances of propagation processes on graphs that are commonly used to model real-world spreading phenomena. The contribution of this paper is two-fold. We first establish a connection between…
Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are…
Rank 1 inhomogeneous random graphs are a natural generalization of Erd\H{o}s R\'enyi random graphs. In this generalization each node is given a weight. Then the probability that an edge is present depends on the product of the weights of…
Empirical contact networks or interaction networks demonstrate peculiar characteristics stemming from the fundamental social, psychological, physical mechanisms governing human interactions. Although these mechanisms are complex, we test…
We include complex connectivity structures and heterogeneity in models of multilayer networks or multilayer hypergraphs growing by preferential attachment. We consider the most generic connectivity structure, where the probability of…
Performance bounds for opportunistic networks have been derived in a number of recent papers for several key quantities, such as the expected delivery time of a unicast message, or the flooding time (a measure of how fast information…
We study a ferromagnetic Ising model on random graphs with a power-law degree distribution and compute the thermodynamic limit of the pressure when the mean degree is finite (degree exponent $\tau>2$), for which the random graph has a…
In this paper, we study the maximum clique problem on hyperbolic random graphs. A hyperbolic random graph is a mathematical model for analyzing scale-free networks since it effectively explains the power-law degree distribution of…
In this paper we derive results concerning the connected components and the diameter of random graphs with an arbitrary i.i.d. degree sequence. We study these properties primarily, but not exclusively, when the tail of the degree…
We consider random hyperbolic graphs in hyperbolic spaces of any dimension $d+1\geq 2$. We present a rescaling of model parameters that casts the random hyperbolic graph model of any dimension to a unified mathematical framework, leaving…
Random hypergraphs extend the classical notion of random graphs by allowing hyperedges to join more than two vertices, making them well-suited for modeling higher-order interactions in complex systems. Despite their broad applicability,…
A bootstrap percolation process on a graph $G$ is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours…
A common way to accelerate shortest path algorithms on graphs is the use of a bidirectional search, which simultaneously explores the graph from the start and the destination. It has been observed recently that this strategy performs…
We study first passage percolation on the configuration model. Assuming that each edge has an independent exponentially distributed edge weight, we derive explicit distributional asymptotics for the minimum weight between two randomly…
Understanding the subgraph distribution in random networks is important for modelling complex systems. In classic Erdos networks, which exhibit a Poissonian degree distribution, the number of appearances of a subgraph G with n nodes and g…
We consider the Bernoulli bond percolation process (with parameter $p$) on infinite graphs and we give a general criterion for bounded degree graphs to exhibit a non-trivial percolation threshold based either on a single isoperimetric…
We investigate the degree distribution resulting from graph generation models based on rank-based attachment. In rank-based attachment, all vertices are ranked according to a ranking scheme. The link probability of a given vertex is…