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We extend the classical preferential attachment random graph model to random simplicial complexes. At each stage of the model, we choose one of the existing $k$-simplices with probability proportional to its $k$-degree. The chosen…
We include complex connectivity structures and heterogeneity in models of multilayer networks or multilayer hypergraphs growing by preferential attachment. We consider the most generic connectivity structure, where the probability of…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…
Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference,for instance GLM techniques, and model verification methods will require knowing test statistics are…
Degree assortativity refers to the increased or decreased probability of connecting two neurons based on their in- or out-degrees, relative to what would be expected by chance. We investigate the effects of such assortativity in a network…
We introduce a new class of deterministic networks by associating networks with Diophantine equations, thus relating network topology to algebraic properties. The network is formed by representing integers as vertices and by drawing cliques…
We develop a progressive training approach for neural networks which adaptively grows the network structure by splitting existing neurons to multiple off-springs. By leveraging a functional steepest descent idea, we derive a simple…
Many complex networks from the World-Wide-Web to biological networks are growing taking into account the heterogeneous features of the nodes. The feature of a node might be a discrete quantity such as a classification of a URL document as…
Network growth as described by the Duplication-Divergence model proposes a simple general idea for the evolution dynamics of natural networks. In particular it is an alternative to the well known Barab\'asi-Albert model when applied to…
Many complex natural and physical systems exhibit patterns of interconnection that conform, approximately, to a network structure referred to as scale-free. Preferential attachment is one of many algorithms that have been introduced to…
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…
A key problem in the study and design of complex systems is the apparent disconnection between the microscopic and the macroscopic. It is not straightforward to identify the local interactions that give rise to an observed global…
Relay selection for cooperative communications promises significant performance improvements, and is, therefore, attracting considerable attention. While several criteria have been proposed for selecting one or more relays, distributed…
One of the best-known models in network science is preferential attachment. In this model, the probability of attaching to a node depends on the degree of all nodes in the population, and thus depends on global information. In many…
The study of community networks has attracted considerable attention recently. In this paper, we propose an evolving community network model based on local processes, the addition of new nodes intra-community and new links intra- or…
We study the organization and dynamics of growing directed networks. These networks are built by adding nodes successively in such a way that each new node has $K$ directed links to the existing ones. The organization of a growing directed…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…
We study the basic preferential attachment process, which generates a sequence of random trees, each obtained from the previous one by introducing a new vertex and joining it to one existing vertex, chosen with probability proportional to…