相关论文: Effect of Closed Paths in Complex networks on Six …
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…
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…
We reformulated the string formalism given by Aoyama, using an adjacent matrix of a network and introduced a series of generalized clustering coefficients based on it. Furthermore we numerically evaluated Milgram condition proposed by their…
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 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…
The purpose of this paper is to assess the statistical characterization of weighted networks in terms of the generalization of the relevant parameters, namely average path length, degree distribution and clustering coefficient. Although the…
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…
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…
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…
A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a…
We present the mathematical analysis of generalized complex contagions in clustered multiplex networks for susceptible-infected-recovered (SIR)-like dynamics. The model is intended to understand diffusion of influence, or any other…
Correlations may affect propagation processes on complex networks. To analyze their effect, it is useful to build ensembles of networks constrained to have a given value of a structural measure, such as the degree-degree correlation $r$,…
The proposal of Six Degrees of Separation makes people realize that the world is not as big as we imagined. Even if the world's population now exceeds 7 billion, two strangers can still get in touch through a limited intermediary. When…
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…
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…
It has been shown that many complex networks shared distinctive features, which differ in many ways from the random and the regular networks. Although these features capture important characteristics of complex networks, their applicability…
Most real complex networks -- such as protein interactions, social contacts, the internet -- are only partially known and available to us. While the process of exploring such networks in many cases resembles a random walk, it becomes a key…
Recently, contagion-based (disease, information, etc.) spreading on social networks has been extensively studied. In this paper, other than traditional full interaction, we propose a partial interaction based spreading model, considering…
Many networks exhibit the small-world property of the neighborhood connectivity being higher than in comparable random networks. However, the standard measure of local neighborhood clustering is typically not defined if a node has one or no…
Frigyes Karinthy, in his 1929 short story "L\'aancszemek" ("Chains") suggested that any two persons are distanced by at most six friendship links. (The exact wording of the story is slightly ambiguous: "He bet us that, using no more than…