Related papers: How to construct a correlated net
In an affiliation network vertices are linked to attributes and two vertices are declared adjacent whenever they share a common attribute. For example, two customers of an internet shop are called adjacent if they have purchased the same or…
We provide a general framework for analyzing degree correlations between nodes separated by more than one step (i.e., beyond nearest neighbors) in complex networks. One probability and four conditional probabilities are introduced to fully…
This research is about studying and comparing two different ways of building complex networks. The main goal of our study is to find an effective way to build networks, particularly when we have fewer observations than variables. We…
We apply a Bethe-Peierls approach to statistical-mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices. Using the NP-hard optimization problem of…
We introduce a broad class of multi-hooking networks, wherein multiple copies of a seed are hooked at each step at random locations, and the number of copies follows a predetermined building sequence of numbers. We analyze the degree…
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…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
We define a growing model of random graphs. Given a sequence of nonnegative integers $\{d_n\}_{n=0}^\infty$ with the property that $d_i\leq i$, we construct a random graph on countably infinitely many vertices $v_0,v_1\ldots$ by the…
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…
The quantum internet is a rapidly developing technological reality, yet, it remains unclear what kind of quantum network structures might emerge. Since indirect quantum communication is already feasible and preserves absolute security of…
We consider distributed networks, such as peer-to-peer networks, whose structure can be manipulated by adjusting the rules by which vertices enter and leave the network. We focus in particular on degree distributions and show that, with…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules.…
Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the…
This work introduces a systematic algorithm for generating directed networks with prescribed symmetries by constructing expansions from a given quotient network. The method enables researchers to synthesize realistic network models with…
Recently, the first author proposed a measure to calculate Pearson correlations for node values expressed in a network, by taking into account distances or metrics defined on the network. In this technical note, we show that using an…
We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Every node is assigned an a-priori i.i.d. fitness with…
We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…
We study a simple model of dynamic networks, characterized by a set preferred degree, $\kappa$. Each node with degree $k$ attempts to maintain its $\kappa$ and will add (cut) a link with probability $w(k;\kappa)$ ($1-w(k;\kappa)$). As a…
Flexible network design deals with building a network that guarantees some connectivity requirements between its vertices, even when some of its elements (like vertices or edges) fail. In particular, the set of edges (resp. vertices) of a…