Distribution of Maximal Clique Size under the Watts-strogatz Model of Evolution of Complex Networks
نویسنده
چکیده
In this paper, we analyze the evolution of a small-world network and its subsequent transformation to a random network using the idea of link rewiring under the well-known Watts-Strogatz model for complex networks. Every link u-v in the regular network is considered for rewiring with a certain probability and if chosen for rewiring, the link u-v is removed from the network and the node u is connected to a randomly chosen node w (other than nodes u and v). Our objective in this paper is to analyze the distribution of the maximal clique size per node by varying the probability of link rewiring and the degree per node (number of links incident on a node) in the initial regular network. For a given probability of rewiring and initial number of links per node, we observe the distribution of the maximal clique per node to follow a Poisson distribution. We also observe the maximal clique size per node in the small-world network to be very close to that of the average value and close to that of the maximal clique size in a regular network. There is no appreciable decrease in the maximal clique size per node when the network transforms from a regular network to a small-world network. On the other hand, when the network transforms from a small-world network to a random network, the average maximal clique size value decreases significantly.
منابع مشابه
Distribution of maximal clique size of the vertices for theoretical small-world networks and real-world networks
Our primary objective in this paper is to study the distribution of the maximal clique size of the vertices in complex networks. We define the maximal clique size for a vertex as the maximum size of the clique that the vertex is part of and such a clique need not be the maximum size clique for the entire network. We determine the maximal clique size of the vertices using a modified version of a...
متن کاملThe Watts–Strogatz network model developed by including degree distribution: theory and computer simulation
By using theoretical analysis and computer simulations, we develop the Watts– Strogatz network model by including degree distribution, in an attempt to improve the comparison between characteristic path lengths and clustering coefficients predicted by the original Watts–Strogatz network model and those of the real networks with the small-world property. Good agreement between the predictions of...
متن کاملConstructing a Watts-Strogatz network from a small-world network with symmetric degree distribution
Though the small-world phenomenon is widespread in many real networks, it is still challenging to replicate a large network at the full scale for further study on its structure and dynamics when sufficient data are not readily available. We propose a method to construct a Watts-Strogatz network using a sample from a small-world network with symmetric degree distribution. Our method yields an es...
متن کاملA Small-world Network Where All Nodes Have the Same Connectivity, with Application to the Dynamics of Boolean Interacting Automata
This paper introduces the equal number of links (ENL) algorithm to generate small-world networks starting from a regular lattice, by randomly rewiring some connections. The approach is similar to the well-known Watts–Strogatz (WS) model, but the present method is different as it leaves the number of connections k of each node unchanged, while the WS algorithm gives rise to a Poisson distributio...
متن کاملNonextensive aspects of small - world networks 1
We have discussed the nonextensive aspects of degree distribution P (k) in Watts-Strogatz (WS) small-world networks by using the three approaches: (a) the maximum-entropy method, (b) hidden-variable distribution and (c) stochastic differential equation. In the method (a), P (k) in complex networks has been obtained by maximizing the nonexten-sive information entropy with the constraint of < k 2...
متن کامل