Related papers: A note on the vertex degree distribution of random…

Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance…

Real networks are often dynamic. In response to it, analyses of algorithms on {\em dynamic networks} attract more and more attentions in network science and engineering. Random walks on dynamic graphs also have been investigated actively in…

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…

Komlos [Tiling Turan theorems, Combinatorica, 20,2 (2000), 203{218] determined the asymptotically optimal minimum degree condition for covering a given proportion of vertices of a host graph by vertex-disjoint copies of a fixed graph. We…

Correlations of active and passive random intersection graphs are studied in this letter. We present the joint probability generating function for degrees of $G^{active}(n,m,p)$ and $G^{passive}(n,m,p)$, which are generated by a random…

We prove an asymptotic formula for the number of orientations with given out-degree (score) sequence for a graph $G$. The graph $G$ is assumed to have average degrees at least $n^{1/3 + \varepsilon}$ for some $\varepsilon > 0$, and to have…

We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates for the mean and variance of the limiting probability distribution and the…

We study the asymptotic properties of distributed consensus algorithms over switching directed random networks. More specifically, we focus on consensus algorithms over independent and identically distributed, directed random graphs, where…

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…

We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…

Quite often real-world networks can be thought of as being symmetric, in the abstract sense that vertices can be found to have similar or equivalent structural roles. However, traditional measures of symmetry in graphs are based on their…

Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…

We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…

We show that the expected gonality of a random graph is asymptotic to the number of vertices.

We give an asymptotic expression for the expected number of spanning trees in a random graph with a given degree sequence $\boldsymbol{d}=(d_1,\ldots, d_n)$, provided that the number of edges is at least $n + \textstyle{\frac{1}{2}}…

In this paper, the leading term of the asymptotics of the number of possible final positions of a random walk on a directed Hamiltonian metric graph is found. Consideration of such dynamical systems could be motivated by problems of…

We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…

In this paper, we analyze the exact asymptotic behavior of the connectivity probability in a random binomial bipartite graph $G(n,m,p)$ under various regimes of the edge probability $p=p(n)$. To determine this probability, a method based on…

In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties…

The vertex isoperimetric number of a graph $G=(V,E)$ is the minimum of the ratio $|\partial_{V}U|/|U|$ where $U$ ranges over all nonempty subsets of $V$ with $|U|/|V|\le u$ and $\partial_{V}U$ is the set of all vertices adjacent to $U$ but…