Related papers: Polynomial growth in degree-dependent first passag…
Human to human transmissible infectious diseases spread in a population using human interactions as its transmission vector. The early stages of such an outbreak can be modeled by a graph whose edges encode these interactions between…
Graph generative models have broad applications in biology, chemistry and social science. However, modelling and understanding the generative process of graphs is challenging due to the discrete and high-dimensional nature of graphs, as…
We introduce a process where a connected rooted multigraph evolves by splitting events on its vertices, occurring randomly in continuous time. When a vertex splits, its incoming edges are randomly assigned between its offspring and a…
We study a combinatorial model of the spread of influence in networks that generalizes existing schemata recently proposed in the literature. In our model, agents change behaviors/opinions on the basis of information collected from their…
In the random $r$-neighbour bootstrap percolation process on a graph $G$, a set of initially infected vertices is chosen at random by retaining each vertex of $G$ independently with probability $p\in (0,1)$, and "healthy" vertices get…
We consider the open problem concerning the possible lack of concentration of the degree distribution in preferential attachment graphs with random initial degree, when its distribution is characterized by extremely heavy tails of power-law…
We study a natural growth process with competition, modeled by two first passage percolation processes, $FPP_1$ and $FPP_\lambda$, spreading on a graph. $FPP_1$ starts at the origin and spreads at rate $1$, whereas $FPP_\lambda$ starts from…
Many hard algorithmic problems dealing with graphs, circuits, formulas and constraints admit polynomial-time upper bounds if the underlying graph has small treewidth. The same problems often encourage reducing the maximal degree of vertices…
Bootstrap percolation on a graph with infection threshold $r\in \mathbb{N}$ is an infection process, which starts from a set of initially infected vertices and in each step every vertex with at least $r$ infected neighbours becomes…
Broadcasting algorithms are important building blocks of distributed systems. In this work we investigate the typical performance of the classical and well-studied push model. Assume that initially one node in a given network holds some…
We consider first-passage percolation on the edges of $\mathbb{Z}^2 \times k,$ namely the slab of width $k$. Each edge is assigned independently a passage time of either 0 (with probability $1-p_c(\mathbb{S}_k)$) or 1 ((with probability…
Many real-world networks exhibit the so-called small-world phenomenon: their typical distances are much smaller than their sizes. One mathematical model for this phenomenon is a long-range percolation graph on a $d$-dimensional box $\{0, 1,…
We generalize the asymptotic behavior of the graph distance between two uniformly chosen nodes in the configuration model to a wide class of random graphs. Among others, this class contains the Poissonian random graph, the expected degree…
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…
In this work we consider a growing random graph sequence where a new vertex is less likely to join to an existing vertex with high degree and more likely to join to a vertex with low degree. In contrast to the well studied…
We give a general existence and convergence result for interacting particle systems on locally finite graphs with possibly unbounded degrees or jump rates. We allow the local state space to be Polish, and the jumps at a site to affect the…
We provide a sufficient condition on the isoperimetric properties of a regular graph $G$ of growing degree $d$, under which the random subgraph $G_p$ typically undergoes a phase transition around $p=\frac{1}{d}$ which resembles the…
Solving optimization problems leads to elegant and practical solutions in a wide variety of real-world applications. In many of those real-world applications, some of the information required to specify the relevant optimization problem is…
Our main result is an extension of Pansu's theorem to random metrics, where the edges of the Cayley are i.i.d. random variable with some finite exponential moment. Based on a previous work by the second author, the proof relies on…
We deal with a general preferential attachment graph model with multiple type edges. The types are chosen randomly, in a way that depends on the evolution of the graph. In the $N$-type case, we define the (generalized) degree of a given…