Related papers: Weights of Cliques in a Random Graph Model Based o…
In this paper, we first review the weighted-versiion of the handshaking lemma based on the idea of a weighted vertex-edge incidence matrix of a given graph $G$. Then, we obtain a generalized version of the handshaking lemma based on the…
This paper proposes a new algorithm for solving maximal cliques for simple undirected graphs using the theory of prime numbers. A novel approach using prime numbers is used to find cliques and ends with a discussion of the algorithm.
For most technical networks, the interplay of dynamics, traffic and topology is assumed crucial to their evolution. In this paper, we propose a traffic-driven evolution model of weighted technological networks. By introducing a general…
In this paper, we consider a weighted generalization of the chromatic number of a Binomial random graph~\(G.\) We equip each edge with a random weight and then colour the vertices in such a way that the absolute colour difference between…
Evolutionary game dynamics in structured populations has been extensively explored in past decades. However, most previous studies assume that payoffs of individuals are fully determined by the strategic behaviors of interacting parties and…
We study graphs whose chromatic number is close to the order of the graph (the number of vertices). Both when the chromatic number is a constant multiple of the order and when the difference of the chromatic number and the order is a small…
Weight thresholding is a simple technique that aims at reducing the number of edges in weighted networks that are otherwise too dense for the application of standard graph theoretical methods. We show that the group structure of real…
The weight of the minimum spanning tree in a complete weighted graph with random edge weights is a well-known problem. For various classes of distributions, it is proved that the weight of the minimum spanning tree tends to a constant,…
This work is a study of the properties of collaboration networks employing the formalism of weighted graphs to represent their one-mode projection. The weight of the edges is directly the number of times that a partnership has been…
Three models of growing random networks with fitness dependent growth rates are analysed using the rate equations for the distribution of their connectivities. In the first model (A), a network is built by connecting incoming nodes to nodes…
In this work we study the behavior of classical two-person, two-strategies evolutionary games on a class of weighted networks derived from Barab\'asi-Albert and random scale-free unweighted graphs. Using customary imitative dynamics, our…
Can one hear the 'sound' of a growing network? We address the problem of recognizing the topology of evolving biological or social networks. Starting from percolation theory, we analytically prove a linear inverse relationship between two…
This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes and degree distributions, identifying four regimes: (i) a dense…
Structural properties of evolving random graphs are investigated. Treating linking as a dynamic aggregation process, rate equations for the distribution of node to node distances (paths) and of cycles are formulated and solved analytically.…
In the theory of dense graph limits, a graphon is a symmetric measurable function $W:[0,1]^2\to [0,1]$. Each graphon gives rise naturally to a random graph distribution, denoted $\mathbb{G}(n,W)$, that can be viewed as a generalization of…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
Weighted graphs are ubiquitous throughout biology, chemistry, and the social sciences, motivating the development of generative models for abstract weighted graph data using deep neural networks. However, most current deep generative models…
A natural representation of random graphs is the random measure. The collection of product random measures, their transformations, and non-negative test functions forms a general representation of the collection of non-negative weighted…
We consider a model of random tree growth, where at each time unit a new vertex is added and attached to an already existing vertex chosen at random. The probability with which a vertex with degree $k$ is chosen is proportional to $w(k)$,…
The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such…