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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…
In multiplex networks with a large number of layers, the nodes can have different activities, indicating the total number of layers in which the nodes are present. Here we model multiplex networks with heterogeneous activity of the nodes…
In this paper we extend our previous results on the connectivity functions and pressure of the Random Cluster Model in the highly subcritical phase and in the highly supercritical phase, originally proved only on the cubic lattice $\Z^d$,…
A bredge (bridge-edge) is an edge whose deletion would split the network component on which it resides into two components. Bredges are vulnerable links that play an important role in network collapse processes, which may result from node…
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…
We propose a modeling framework for growing multiplexes where a node can belong to different networks. We define new measures for multiplexes and we identify a number of relevant ingredients for modeling their evolution such as the coupling…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
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 study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant $n$. Under mild assumptions on the non-linearity, we obtain…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem.…
We study distributed computation in synchronous dynamic networks where an omniscient adversary controls the unidirectional communication links. Its behavior is modeled as a sequence of directed graphs representing the active (i.e. timely)…
We propose a model to create synthetic networks that may also serve as a narrative of a certain kind of infrastructure network evolution. It consists of an initialization phase with the network extending tree-like for minimum cost and a…
Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…
We solve the weak percolation problem for multiplex networks with overlapping edges. In weak percolation, a vertex belongs to a connected component if at least one of its neighbors in each of the layers is in this component. This is a…
Complex networks have recently aroused a lot of interest. However, network edges are considered to be the same in almost all these studies. In this paper, we present a simple classification method, which divides the edges of undirected,…
In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…
We consider distributed detection problems over adaptive networks, where dispersed agents learn continually from streaming data by means of local interactions. The simultaneous requirements of adaptation and cooperation are achieved by…
Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…
Bipartite (two-mode) networks are important in the analysis of social and economic systems as they explicitly show conceptual links between different types of entities. However, applications of such networks often work with a projected…