Related papers: Quantitative modeling of degree-degree correlation…
We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
We investigate degree correlations in two online social networks where users are connected through different types of links. We find that, while subnetworks in which links have a positive connotation, such as endorsement and trust, are…
In this paper, a random clique network model to mimic the large clustering coefficient and the modular structure that exist in many real complex networks, such as social networks, artificial networks, and protein interaction networks, is…
Complex networks across various fields are often considered to be scale free -- a statistical property usually solely characterized by a power-law distribution of the nodes' degree $k$. However, this characterization is incomplete. In…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
We apply the degree formula for connective $K$-theory to study rational contractions of algebraic varieties. Examples include rationally connected varieties and complete intersections.
Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modeled in tractable network models, creating an obstacle to the theoretical understanding…
We study collaboration networks in terms of evolving, self-organizing bipartite graph models. We propose a model of a growing network, which combines preferential edge attachment with the bipartite structure, generic for collaboration…
We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated…
It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and they are also scale-free (the degrees are distributed according to a power…
In a recent work \cite{LiuJoladSchZia13}, we introduced dynamic networks with preferred degrees and presented simulation and analytic studies of a single, homogeneous system as well as two interacting networks. Here, we extend these studies…
The use of degree-degree correlations to model realistic networks which are characterized by their Pearson's coefficient, has become widespread. However the effect on how different correlation algorithms produce different results on…
The degree-degree correlation is important in understanding the structural organization of a network and the dynamics upon a network. Such correlation is usually measured by the assortativity coefficient $r$, with natural bounds $r \in…
Network data sets are often constructed by some kind of thresholding procedure. The resulting networks frequently possess properties such as heavy-tailed degree distributions, clustering, large connected components and short average…
We propose a generalization of the concept of assortativity based on the tensorial representation of multilayer networks, covering the definitions given in terms of Pearson and Spearman coefficients. Our approach can also be applied to…
We deal with a general preferential attachment graph model with multiple type edges. The types are chosen randomly, in a way that depends on the evolution of the graph. In the $N$-type case, we define the (generalized) degree of a given…
We introduce a dynamical network model which unifies a number of network families which are individually known to exhibit $q$-exponential degree distributions. The present model dynamics incorporates static (non-growing) self-organizing…
The interactions among the elementary components of many complex systems can be qualitatively different. Such systems are therefore naturally described in terms of multiplex or multi-layer networks, i.e. networks where each layer stands for…
The Japanese shareholding network at the end of March 2002 is studied. To understand the characteristics of this network intuitively, we visualize it as a directed graph and an adjacency matrix. Especially detailed features of networks…