相关论文: Asymptotic distribution of degree--based topologic…

We revisit the problem of designing sublinear algorithms for estimating the average degree of an $n$-vertex graph. The standard access model for graphs allows for the following queries: sampling a uniform random vertex, the degree of a…

Topological indices are graph invariants numeric quantities, which are utilized by researchers to analyze a variety of physiochemical aspects of molecules. The goal of developing topological indices is to give each chemical structure a…

In this work we perform a detailed statistical analysis of topological and spectral properties of random geometric graphs (RGGs); a graph model used to study the structure and dynamics of complex systems embedded in a two dimensional space.…

We consider two independent Erd\H{o}s-R\'enyi random graphs, with possibly different parameters, and study two isomorphism problems, a graph embedding problem and a common subgraph problem. Under certain conditions on the graph parameters…

Inhomogeneous Erd\H{o}s-R\'enyi random graphs $\mathbb G_N$ on $N$ vertices in the non-dense regime are considered in this paper. The edge between the pair of vertices $\{i,j\}$ is retained with probability…

For the Erd\H{o}s-R\'enyi random graph G(n,p), we give a precise asymptotic formula for the size of a largest vertex subset in G(n,p) that induces a subgraph with average degree at most t, provided that p = p(n) is not too small and t =…

Let $G$ be a simple graph with $n$ vertices and let $$C(G;x)=\sum_{k=0}^n(-1)^{n-k}c(G,k)x^k$$ denote the Laplacian characteristic polynomial of $G$. Then if the size $|E(G)|$ is large compared to the maximum degree $\Delta(G)$, Laplacian…

We study a variant of the standard random intersection graph model ($G(n,m,F,H)$) in which random weights are assigned to both vertex types in the bipartite structure. Under certain assumptions on the distributions of these weights, the…

This paper introduces the concept of compliant vertices and compliant graphs, with a focus on the total domination degree (TDD) of a vertex in compliant graphs. The TDD is systematically calculated for various graph classes, including path…

Chemical graphs are simple undirected connected graphs, where vertices represent atoms in a molecule and edges represent chemical bonds. A degree-based topological index is a molecular descriptor used to study specific physicochemical…

The bivariate distribution of degrees of adjacent vertices (degree-degree distribution) is an important network characteristic defining the statistical dependencies between degrees of adjacent vertices. We show the asymptotic degree-degree…

We establish asymptotic vertex degree distribution and examine its relation to the clustering coefficient in two popular random intersection graph models of Godehardt and Jaworski [Electron. Notes Discrete Math. 10 (2001) 129-132]. For…

We consider random graphs on the set of $N^2$ vertices placed on the discrete $2$-dimensional torus. The edges between pairs of vertices are independent, and their probabilities decay with the distance $\rho$ between these vertices as…

In this paper, we study some important statistics of the random graph in the directed preferential attachment model introduced by B. Bollob\'as, C. Borgs, J. Chayes and O. Riordan. First, we find a new asymptotic formula for the expectation…

The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…

We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A…

This article presents the precise asymptotical distribution of two types of critical transmission radii, defined in terms of k-connectivity and the minimum vertex degree, for random geometry graphs distributed over three-dimensional…

Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…

We study mesoscopic signatures of the topological Anderson transitions in topological disordered chains. To this end we introduce an integer-valued sample-specific definition of the topological index in finite size systems. Its phase…

Continuing the recent work of L. Zhong and K. Xu [MATCH Commun. Math. Comput. Chem.71(2014) 627-642], we determine inequalities among several vertex-degree-based topological indices; first geometric-arithmetic index(GA), augmented Zagreb…