Related papers: A Markov Chain-Based Numerical Method for Calculat…
Many real networks such as the World Wide Web, financial, biological, citation and social networks have a power-law degree distribution. Networks with this feature are also called scale-free. Several models for producing scale-free networks…
In networking applications, one often wishes to obtain estimates about the number of objects at different parts of the network (e.g., the number of cars at an intersection of a road network or the number of packets expected to reach a node…
The degree distribution is an important characteristic of complex networks. In many data analysis applications, the networks should be represented as fixed-length feature vectors and therefore the feature extraction from the degree…
Degree distributions of graph representations for compact urban patterns are scale-dependent. Therefore, the degree statistics alone does not give us the enough information to reach a qualified conclusion on the structure of urban spatial…
This work reports the most relevant technical aspects in the problem of learning the \emph{Markov network structure} from data. Such problem has become increasingly important in machine learning, and many other application fields of machine…
The rich-club phenomenon, which provides information about the association between nodes, is a useful method to study the hierarchy structure of networks. In this work, we explore the behavior of rich-club coefficient (RCC) in scale-free…
We present a novel type of weighted scale-free network model, in which the weight grows independently of the attachment of new nodes. The evolution of this network is thus determined not only by the preferential attachment of new nodes to…
In network modeling of complex systems one is often required to sample random realizations of networks that obey a given set of constraints, usually in form of graph measures. A much studied class of problems targets uniform sampling of…
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…
Complex networks have gained more attention from the last few years. The size of real-world complex networks, such as online social networks, WWW network, collaboration networks, is increasing exponentially with time. It is not feasible to…
This paper introduces a method to generate hierarchically modular networks with prescribed node degree list and proposes a metric to measure network modularity based on the notion of edge distance. The generated networks are used as test…
Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks…
Decentralized stochastic gradient method emerges as a promising solution for solving large-scale machine learning problems. This paper studies the decentralized Markov chain gradient descent (DMGD) algorithm - a variant of the decentralized…
This article discusses the properties of extremes of degree sequences calculated from network data. We introduce the notion of a normalized degree, in order to permit a comparison of degree sequences between networks with differing numbers…
We study the realizability of scale free-networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this…
We introduce a Markov Chain Monte Carlo algorithm which samples from the space of spanning trees of complete graphs using local rewiring operations only. The probability distribution of graphs of this kind is shown to depend on the…
Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow $p(k)\sim ck^{-\alpha}$. We study the robustness of scale-free networks to random…
In this work we study a simple evolutionary model of bipartite networks which its evolution is based on the duplication of nodes. Using analytical results along with numerical simulation of the model, we show that the above evolutionary…
There is a pressing need for a description of complex systems that includes considerations of the underlying network of interactions, for a diverse range of biological, technological and other networks. In this work relationships between…
Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model…