Related papers: Optimization and Scale-freeness for Complex Networ…

Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of the number of times a small connected graph occurs as a…

Many realistic networks are scale-free, with small characteristic path lengths, high clustering, and power law in their degree distribution. They can be obtained by dynamical networks in which a preferential attachment process takes place.…

In a recursive way and by including a parameter, we introduce a family of deterministic scale-free networks. The resulting networks exhibit small-world effects. We calculate the exact results for the degree exponent, the clustering…

We consider a class of simple, non-trivial models of evolving weighted scale-free networks. The network evolution in these models is determined by attachment of new vertices to ends of preferentially chosen weighted edges. Resulting…

All networks can be analyzed at multiple scales. A higher scale of a network is made up of macro-nodes: subgraphs that have been grouped into individual nodes. Recasting a network at higher scales can have useful effects, such as decreasing…

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…

We discuss how various models of scale-free complex networks approach their limiting properties when the size N of the network grows. We focus mainly on equilibrated networks and their finite-size degree distributions. Our results show that…

Existing information-theoretic frameworks based on maximum entropy network ensembles are not able to explain the emergence of heterogeneity in complex networks. Here, we fill this gap of knowledge by developing a classical framework for…

When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or…

We study localization of information on scale free networks with communication constraints when, for some reason, information can propagate only between ``mutually trusted nodes'' (MTN). We propose an algorithm to construct the MTN network…

There are many networks in real life which exist as form of Scale-free networks such as World Wide Web, protein-protein interaction network, semantic networks, airline networks, interbank payment networks, etc. If we want to analyze these…

When large scale training data is available, one can obtain compact and accurate networks to be deployed in resource-constrained environments effectively through quantization and pruning. However, training data are often protected due to…

Empirical complex systems must differentially respond to external perturbations and, at the same time, internally distribute information to coordinate their components. While networked backbones help with the latter, they limit the…

A network is formed using the $N$ sites of an one-dimensional lattice in the shape of a ring as nodes and each node with the initial degree $k_{in}=2$. $N$ links are then introduced to this network, each link starts from a distinct node,…

We introduce a simple one-parameter network growth algorithm which is able to reproduce a wide variety of realistic network structures but without having to invoke any global information about node degrees such as preferential-attachment…

We consider the problem of identifying the most influential nodes for a spreading process on a network when prior knowledge about structure and dynamics of the system is incomplete or erroneous. Specifically, we perform a numerical analysis…

We describe an ensemble of growing scale-free networks in an equilibrium framework, providing insight into why the exponent of empirical scale-free networks in nature is typically robust. In an analogy to thermostatistics, to describe the…

We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…

We propose an information-based model for network dynamics in which imperfect information leads to networks where the different vertices have widely different number of edges to other vertices, and where the topology has hierarchical…

We study the topology of e-mail networks with e-mail addresses as nodes and e-mails as links using data from server log files. The resulting network exhibits a scale-free link distribution and pronounced small-world behavior, as observed in…