Related papers: Link and subgraph likelihoods in random undirected…
One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands such as the Minimum $k$-Edge-Connected Spanning Subgraph problem ($k$-ECSS), as well as nonuniform…
In complex networks the rich nodes are the subset of nodes with high degree. These well connected nodes tend to dominate the organisation of the network's structure. In non-evolving networks, a reference network has been used to detect if…
In this paper we theoretically and empirically study the degree and connectivity of the Internet's scale-free topology at the autonomous system (AS) level. The basic features of the scale-free network have influence on the normalization…
We present a systematic and detailed study of the robustness of directed networks under random and targeted removal of links. We work with a set of network models of random and scale free type, generated with specific features of clustering…
Dyadic network formation models have wide applicability in economic research, yet are difficult to estimate in the presence of individual specific effects and in the absence of distributional assumptions regarding the model noise component.…
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…
We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
We propose that negative degree correlation among nodes in a network of nonlinear oscillators, often detected in real world networks, is motivated by its positive effects on synchronizability. In so doing, we use a novel methodology to…
Subgraphs such as cliques, loops and stars form crucial connections in the topologies of real-world networks. Random graph models provide estimates for how often certain subgraphs appear, which in turn can be tested against real-world…
This paper discusses the reliability of a graph in which the links are perfectly reliable but the nodes may fail with certain probability p. Calculating graph node reliability is an NP-Hard problem. We introduce an efficient and accurate…
Despite the growing interest in characterizing the local geometry leading to the global topology of networks, our understanding of the local structure of complex networks, especially real-world networks, is still incomplete. Here, we…
We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the…
We are interested in the probability that two randomly selected neighbors of a random vertex of degree (at least) $k$ are adjacent. We evaluate this probability for a power law random intersection graph, where each vertex is prescribed a…
We developed a scheme for evaluating the size of the largest connected subnetwork (giant component) in random networks and the percolation threshold when sites (nodes) and/or bonds (edges) are removed from the networks based on the cavity…
Estimating network formation models with degree heterogeneity raises two problems in empirical networks. First, agents that send no links, receive no links, or link to all remaining agents can make the fixed-effects MLE fail to exist.…
Random graph null models have found widespread application in diverse research communities analyzing network datasets, including social, information, and economic networks, as well as food webs, protein-protein interactions, and neuronal…
In this paper we construct and analyse strongly connected sparse directed networks with an enhanced propensity for synchronization (PFS). Two types of PFS-enhanced networks are considered: (i) an eigenratio minimizing ensemble with…
It is commonly believed that scale-free networks are robust to massive numbers of random node deletions. For example, Cohen et al. study scale-free networks including some which approximate the measured degree distribution of the Internet.…
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,…