Related papers: The diameter of KPKVB random graphs
In a recursive way and by including a parameter, we introduce a family of deterministic scale-free networks. The resulting networks exhibit small-world effects. We calculate the exact results for the degree exponent, the clustering…
The Barab\'{a}si-Albert (BA) model is extended to include the concept of local world and the microscopic event of adding edges. With probability $p$, we add a new node with $m$ edges which preferentially link to the nodes presented in the…
Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…
In the past two decades, a series of important results have been established in the empirical and theoretical modeling of complex networks, although considered are mainly pairwise networks. However, with the development of science and…
Network science have constantly been in the focus of research for the last decade, with considerable advances in the controllability of their structural. However, much less effort has been devoted to study that how to improve the…
We propose a model that generates a new class of networks exhibiting power-law degree distribution with a spectrum of exponents depending on the number of links ($m$) with which incoming nodes join the existing network. Unlike the…
One interesting question is how a graph develops from some constrained random graph process, which is a fundamental mechanism in the formation and evolution of dynamic networks. The problem here is referred to the random $K_k$-removal…
Adaptive (or co-evolutionary) network dynamics, i.e., when changes of the network/graph topology are coupled with changes in the node/vertex dynamics, can give rise to rich and complex dynamical behavior. Even though adaptivity can improve…
First principle network models are crucial to make sense of the intricate topology of real complex networks. While modeling efforts have been quite successful in undirected networks, generative models for networks with asymmetric…
We consider the model of complex hyperbranched polymer structures formed on the basis of scale-free graphs, where functionalities (degrees) $k$ of nodes obey a power law decaying probability $p(k)\sim{k^{-\alpha}}$. Such polymer topologies…
Capacity scaling laws are analyzed in an underwater acoustic network with $n$ regularly located nodes on a square. A narrow-band model is assumed where the carrier frequency is allowed to scale as a function of $n$. In the network, we…
We revisit the classical question of the relationship between the diameter of a graph and its expansion properties. One direction is well understood: expander graphs exhibit essentially the lowest possible diameter. We focus on the reverse…
Let $G=(V,E)$ be a connected graph with the usual (graph) distance metric $d:V \times V \to N \cup \{0 \}$. Introduced by Gromov, $G$ is $\delta$-hyperbolic if for every four vertices $u,v,x,y \in V$, the two largest values of the three…
Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
A power law degree distribution is established for a graph evolution model based on the graph class of k-trees. This k-tree-based graph process can be viewed as an idealized model that captures some characteristics of the preferential…
Many complex systems--from social and communication networks to biological networks and the Internet--are thought to exhibit scale-free structure. However, prevailing explanations rely on the constant addition of new nodes, an assumption…
The bandwidth of a graph is the labeling of vertices with minimum maximum edge difference. For many graph families this is NP-complete. A classic result computes the bandwidth for the hypercube. We generalize this result to give sharp lower…
In the first part of this paper we determine the maximum size of a (finite, simple, connected) bipartite graph of given order, diameter $d$, and connectivity $\kappa$. It was shown by Ali, Mazorodze, Mukwembi and Vetr\'ik [On size, order,…
We determine the asymptotic growth rate of the diameter of the random hyperbolic surfaces constructed by Brooks and Makover. This model consists of a uniform gluing of $2n$ hyperbolic ideal triangles along their sides followed by a…