Related papers: Cluster Growth in a Growing Tree Network
Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of…
In this paper, we analyze the behavior of the global clustering coefficient in scale free graphs. We are especially interested in the case of degree distribution with an infinite variance, since such degree distribution is usually observed…
A linear bubble model of grain growth is introduced to study the conditions under which an isolated grain can grow to a size much larger than the surrounding matrix average (abnormal growth). We first consider the case of bubbles of two…
We present exact results for a lattice model of cluster growth in 1D. The growth mechanism involves interface hopping and pairwise annihilation supplemented by spontaneous creation of the stable-phase, +1, regions by overturning the…
We develop a network in which the natural numbers are the vertices. We use the decomposition of natural numbers by prime numbers to establish the connections. We perform data collapse and show that the degree distribution of these networks…
We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a…
Large ensembles of globally coupled chaotic neural networks undergo a transition to complete synchronization for high coupling intensities. The onset of this fully coherent behavior is preceded by a regime where clusters of networks with…
We propose a model for evolving networks by merging building blocks represented as complete graphs, reminiscent of modules in biological system or communities in sociology. The model shows power-law degree distributions, power-law…
We investigate bond percolation on the Song-Havlin-Makse (SHM) network, a scale-free tree with a tunable degree exponent and dimensionality. Using a generating function approach, we analytically derive the average size and the fractal…
Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained (see previous work by Bhamidi, van der Hofstad and van Leeuwaarden).…
Scale-free networks arise from power-law degree distributions. Due to the finite size of real-world networks, the power law inevitably has a cutoff at some maximum degree $\Delta$. We investigate the relative size of the giant component $S$…
The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…
We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…
Many real systems exhibit the processes of growth and shrink. In this paper, we propose a network evolution model based on the simultaneous application of both node addition and deletion rules. To obtain a higher clustering that is present…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
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…
We investigate an extremal dynamics model of evolution with a variable number of units. Due to addition and removal of the units, the topology of the network evolves and the network splits into several clusters. The activity is mostly…
We study a social network consisting of over $10^4$ individuals, with a degree distribution exhibiting two power scaling regimes separated by a critical degree $k_{\rm crit}$, and a power law relation between degree and local clustering. We…
Transient dynamics leading to the synchrony of pulse-coupled oscillators has previously been studied as an aggregation process of synchronous clusters, and a rate equation for the cluster size distribution has been proposed. However, the…
We investigate the behavior of large connected components in the Poisson Random Connection model in non-critical regimes with any bounded connection function. We show that the asymptotic size of the largest component restricted to a window…