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A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…

Probability · Mathematics 2015-09-24 Maria Deijfen , Willemien Kets

In this paper, we study the impact of edge weights on distances in diluted random graphs. We interpret these weights as delays, and take them as i.i.d exponential random variables. We analyze the weighted flooding time defined as the…

Probability · Mathematics 2010-11-30 Hamed Amini , Moez Draief , Marc Lelarge

This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions…

Probability · Mathematics 2020-07-14 Christian Hirsch , Sarat B. Moka , Thomas Taimre , Dirk P. Kroese

This paper is centered on the random graph generated by a Doeblin-type coupling of discrete time processes on a countable state space whereby when two paths meet, they merge. This random graph is studied through a novel subgraph, called a…

Probability · Mathematics 2018-11-27 François Baccelli , Mir-Omid Haji-Mirsadeghi , James T. Murphy

We study spreading processes in temporal graphs, i. e., graphs whose connections change over time. These processes naturally model real-world phenomena such as infectious diseases or information flows. More precisely, we investigate how…

Data Structures and Algorithms · Computer Science 2021-07-21 Hendrik Molter , Malte Renken , Philipp Zschoche

We study a family of directed random graphs whose arcs are sampled independently of each other, and are present in the graph with a probability that depends on the attributes of the vertices involved. In particular, this family of models…

Probability · Mathematics 2017-12-12 Junyu Cao , Mariana Olvera-Cravioto

We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…

Combinatorics · Mathematics 2013-11-13 Svante Janson , Simone Severini

In this paper, we present a result similar to the shift-coupling result of Thorisson (1996) in the context of random graphs and networks. The result is that a given random rooted network can be obtained by changing the root of another given…

Probability · Mathematics 2020-01-10 Ali Khezeli

In this paper we focus on the problem of the degree sequence for the following random graph process. At any time-step $t$, one of the following three substeps is executed: with probability $\alpha_1$, a new vertex $x_t$ and $m$ edges…

Probability · Mathematics 2008-07-01 Xian-Yuan Wu , Zhao Dong , Ke Liu , Kai-Yuan Cai

In several settings (e.g., sensor networks and social networks), nodes of a graph are equipped with initial opinions, and the goal is to estimate the average of these opinions using local operations. A natural algorithm to achieve this is…

Probability · Mathematics 2025-04-29 Dor Elboim , Yuval Peres , Ron Peretz

We introduce a broad class of multi-hooking networks, wherein multiple copies of a seed are hooked at each step at random locations, and the number of copies follows a predetermined building sequence of numbers. We analyze the degree…

Probability · Mathematics 2022-05-04 Kiran R. Bhutani , Ravi Kalpathy , Hosam Mahmoud

We introduce a class of random graphs that we argue meets many of the desiderata one would demand of a model to serve as the foundation for a statistical analysis of real-world networks. The class of random graphs is defined by a…

Statistics Theory · Mathematics 2015-12-11 Victor Veitch , Daniel M. Roy

Motivated by limits of critical inhomogeneous random graphs, we construct a family of sequences of measured metric spaces that we call continuous multiplicative graphs, that are expected to be the universal limit of graphs related to the…

Probability · Mathematics 2020-02-07 Nicolas Broutin , Thomas Duquesne , Minmin Wang

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…

Probability · Mathematics 2024-11-06 Hamin Jung

We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated…

Statistical Mechanics · Physics 2010-05-11 Piotr Bialas , Andrzej K. Oleś

We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the…

Probability · Mathematics 2007-11-20 Noga Alon , Chen Avin , Michal Koucky , Gady Kozma , Zvi Lotker , Mark R. Tuttle

A temporal random geometric graph is a random geometric graph in which all edges are endowed with a uniformly random time-stamp, representing the time of interaction between vertices. In such graphs, paths with increasing time stamps…

Probability · Mathematics 2025-02-24 Anna Brandenberger , Serte Donderwinkel , Céline Kerriou , Gábor Lugosi , Rivka Mitchell

We consider the number of common edges in two independent random spanning trees of a graph $G$. For complete graphs $K_n$, we give a new proof of the fact, originally obtained by Moon, that the distribution converges to a Poisson…

Combinatorics · Mathematics 2025-06-09 Miklos Bona , Fabian Burghart , Stephan Wagner

In this paper we consider a simple model of random graph process with {\it hard} copying as follows: At each time step $t$, with probability $0<\alpha\leq 1$ a new vertex $v_t$ is added and $m$ edges incident with $v_t$ are added in the…

Probability · Mathematics 2008-08-05 Gao-Rong Ning , Xian-Yuan Wu , Kai-Yuan Cai

We define the edge reconnecting model, a random multigraph evolving in time. At each time step we change one endpoint of a uniformly chosen edge: the new endpoint is chosen by linear preferential attachment. We consider a sequence of edge…

Probability · Mathematics 2012-04-27 Balazs Rath