Related papers: Random Networks with Tunable Degree Distribution a…
Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…
In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…
Delaunay triangulation can be considered as a type of complex networks. For complex networks, the degree distribution is one of the most important inherent characteristics. In this paper, we first consider the two- and three-dimensional…
Designing algorithms that generate networks with a given degree sequence while varying both subgraph composition and distribution of subgraphs around nodes is an important but challenging research problem. Current algorithms lack control of…
We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution…
An analytical approach to calculating bond percolation thresholds, sizes of $k$-cores, and sizes of giant connected components on structured random networks with non-zero clustering is presented. The networks are generated using a…
Recent years have seen a growing interest in the modeling and simulation of social networks to understand several social phenomena. Two important classes of networks, small world and scale free networks have gained a lot of research…
In this paper, we propose a simple rule that generates scale-free small-world networks with tunable assortative coefficient. These networks are constructed by two-stage adding process for each new node. The model can reproduce scale-free…
In this paper we introduce a model of spatial network growth in which nodes are placed at randomly selected locations on a unit square in $\mathbb{R}^2$, forming new connections to old nodes subject to the constraint that edges do not…
We generalize an algorithm used widely in the configuration model such that power-law degree sequences with the degree exponent $\lambda$ and the number of links per node $K$ controllable independently may be generated. It yields the degree…
Many real networks have cliques as their constitutional units. Here we present a family of scale-free network model consist of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and…
The effects of link rewiring are considered for the class of directed networks where each node has the same fixed out-degree. We model a network generated by three mechanisms that are present in various networked systems; growth, global…
Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. Various tools have been developed over the centuries to discover and study the various patterns in the sequence of…
Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…
Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as…
Motivated by the analysis of social networks, we study a model of random networks that has both a given degree distribution and a tunable clustering coefficient. We consider two types of growth processes on these graphs: diffusion and…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
Using a recently described technique for manipulating the clustering coefficient of a network without changing its degree distribution, we examine the effect of clustering on the synchronization of phase oscillators on networks with Poisson…
We give an intuitive though general explanation of the finite-size effect in scale-free networks in terms of the degree distribution of the starting network. This result clarifies the relevance of the starting network in the final degree…
A network is formed using the $N$ sites of an one-dimensional lattice in the shape of a ring as nodes and each node with the initial degree $k_{in}=2$. $N$ links are then introduced to this network, each link starts from a distinct node,…