Related papers: Random graphs with arbitrary i.i.d. degrees
In this paper we study the degree sequence of the permutation graph $G_{\pi_n}$ associated with a sequence $\pi_n\in S_n$ of random permutations. Joint limiting distributions of the degrees are established using results from graph and…
The average nearest neighbor degree (ANND) of a node of degree $k$ is widely used to measure dependencies between degrees of neighbor nodes in a network. We formally analyze ANND in undirected random graphs when the graph size tends to…
In a network cliques are fully connected subgraphs that reveal which are the tight communities present in it. Cliques of size c>3 are present in random Erdos and Renyi graphs only in the limit of diverging average connectivity. Starting…
We investigate the joint distribution of nodes of small degrees and the degree profile in preferential dynamic attachment circuits. In particular, we study the joint asymptotic distribution of the number of the nodes of outdegree $0$…
Although the spectral properties of random graphs have been a long-standing focus of network theory, the properties of right eigenvectors of directed graphs have so far eluded an exact analytic treatment. We present a general theory for the…
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 consider the set of all graphs on n labeled vertices with prescribed degrees D=(d_1, ..., d_n). For a wide class of tame degree sequences D we prove a computationally efficient asymptotic formula approximating the number of graphs within…
If a vertex $v$ in a graph $G$ has degree larger than the average of the degrees of its neighbors, we call it a groupie in $G$. In the current work, we study the behavior of groupie in random multipartite graphs with the link probability…
We study the random graph obtained by random deletion of vertices or edges from a random graph with given vertex degrees. A simple trick of exploding vertices instead of deleting them, enables us to derive results from known results for…
A random geometric digraph $G_n$ is constructed by taking $\{X_1,X_2,... X_n\}$ in $\mathbb{R}^2$ independently at random with a common bounded density function. Each vertex $X_i$ is assigned at random a sector $S_i$ of central angle…
Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained (see previous work by Bhamidi, van der Hofstad and van Leeuwaarden).…
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…
Radial Moore graphs and digraphs are extremal graphs related to the Moore ones where the distance-preserving spanning tree is preserved for some vertices. This leads to classify them according to their proximity to being a Moore graph or…
The average size of connected vertex subsets of a connected graph generalises a much-studied parameter for subtrees of trees. For trees, the possible values of this parameter are critically affected by the presence or absence of vertices of…
The degree-diameter problem seeks to find the largest possible number of vertices in a graph having given diameter and given maximum degree. Very often the problem is studied for restricted families of graph such as vertex-transitive or…
We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such…
We study an inhomogeneous sparse random graph on [N] = {1, . . . , N } as introduced in a seminal paper by Bollobas, Janson and Riordan (2007): vertices have a type (here in a compact metric space S), and edges between different vertices…
We consider random graphs sampled uniformly from a structured class of graphs, such as the class of graphs embeddable in a given surface. We sharpen and extend earlier results on pendant appearances, concerning for example numbers of…
In the classical Erd\"os-R\'enyi random graph G(n,p) there are n vertices and each of the possible edges is independently present with probability p. The random graph G(n,p) is homogeneous in the sense that all vertices have the same…
In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edges are far from independent, and to prove several results…