Related papers: Separation Number and Generalized Clustering Coeff…

We introduce a series of generalized clustering coefficients based on String formalism given by Aoyama, using adjacent matrix in networks. We numerically evaluate Milgram condition proposed in order to explore q-th degrees of separation in…

The phenomenon of six degrees of separation is an old but interesting problem. The considerations of the clustering coefficient reflecting triangular structures and its extension to square one to six degrees of separation have been…

Milgram Condition proposed by Aoyama et al. plays an important role on the analysis of "six degrees of separation". We have shown that the relations between Milgram condition and the generalized clustering coefficient, which was introduced…

The phenomenon of six degrees of separation is an old but attractive subject. The deep understanding has been uncovered yet, especially how closed paths included in a network affect six degrees of separation are an important subject left…

In this article we discuss six degrees of separation, which has been proposed by Milgram, from a theoretical point of view. Simply if one has $k$ friends, the number $N$ of indirect friends goes up to $\sim k^d$ in $d$ degrees of…

Stanley Milgram's small world experiment presents "six degrees of separation" of our world. One phenomenon of the experiment still puzzling us is that how individuals operating with the social network information with their characteristics…

In this article we discuss six degrees of separation, which has been suggested by Milgram's famous experiment\cite{Milg},\cite{Milg2}, from a theoretical point of view again. Though Milgram's experiment was partly inspired to Pool and…

A wealth of evidence shows that real world networks are endowed with the small-world property i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most…

The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order. Next, we introduce a new class of small…

In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases…

Complex networks has been a hot topic of research over the past several years over crossing many disciplines, starting from mathematics and computer science and ending by the social and biological sciences. Random graphs were studied to…

The Small-World phenomenon, popularly known as six degrees of separation, has been mathematically formalized by Watts and Strogatz in a study of the topological properties of a network. Small-worlds networks are defined in terms of two…

Discoveries of the scale-free and small-world features are reported on a network constructed from the seismic data. It is shown that the connectivity distribution decays as a power law, and the value of the degrees of separation, i.e., 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…

According to the small-world concept, the entire world is connected through short chains of acquaintances. In popular imagination this is captured in the phrase six degrees of separation, implying that any two individuals are, at most, six…

Recently there have been a tremendous interest in models of networks with a power-law distribution of degree -- so called "scale-free networks." It has been observed that such networks, normally, have extremely short path-lengths, scaling…

Various real-life networks of current interest are simultaneously scale-free and modular. Here we study analytically the average distance in a class of deterministically growing scale-free modular networks. By virtue of the recursive…

We give exact relations which are valid for small-world networks (SWN's) with a general `degree distribution', i.e the distribution of nearest-neighbor connections. For the original SWN model, we illustrate how these exact relations can be…

Many networks contain correlations and often conventional analysis is incapable of incorporating this often essential feature. In arXiv:0708.2176, we introduced the link-space formalism for analysing degree-degree correlations in evolving…

We introduce the link-space formalism for analyzing network models with degree-degree correlations. The formalism is based on a statistical description of the fraction of links l_{i,j} connecting nodes of degrees i and j. To demonstrate its…