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We present exact analysis of the physical properties of bimodal networks specified by the two peak degree distribution fully incorporating the degree-degree correlation between node connection. The structure of the correlated bimodal…
One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of…
We study the statistical properties of the sampled scale-free networks, deeply related to the proper identification of various real-world networks. We exploit three methods of sampling and investigate the topological properties such as…
We study non-uniform percolation in a two-dimensional cluster growth model with multiple seeds. With increasing concentration of seeds, the percolation threshold is found to increase monotonically, while the exponents for correlation…
The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…
The k-core decomposition of a network has thus far mainly served as a powerful tool for the empirical study of complex networks. We now propose its explicit integration in a theoretical model. We introduce a Hard-core Random Network model…
Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics.…
The use of degree-degree correlations to model realistic networks which are characterized by their Pearson's coefficient, has become widespread. However the effect on how different correlation algorithms produce different results on…
We study a problem of failure of two interdependent networks in the case of correlated degrees of mutually dependent nodes. We assume that both networks (A and B) have the same number of nodes $N$ connected by the bidirectional dependency…
In this paper, we introduce a new class of stochastic multilayer networks. A stochastic multilayer network is the aggregation of $M$ networks (one per layer) where each is a subgraph of a foundational network $G$. Each layer network is the…
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
Spatial random graphs capture several important properties of real-world networks. We prove quenched results for the continuum space version of scale-free percolation introduced in [DW18]. This is an undirected inhomogeneous random graph…
Most real-world complex systems can be modelled by coupled networks with multiple layers. How and to what extent the pattern of couplings between network layers may influence the interlaced structure and function of coupled networks are not…
Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…
The study of percolation in so-called {\em nested subgraphs} implies a generalization of the concept of percolation since the results are not linked to specific graph process. Here the behavior of such graphs at criticallity is studied for…
We discuss three related models of scale-free networks with the same degree distribution but different correlation properties. Starting from the Barabasi-Albert construction based on growth and preferential attachment we discuss two other…
Random-cluster measures on infinite regular trees are studied in conjunction with a general type of `boundary condition', namely an equivalence relation on the set of infinite paths of the tree. The uniqueness and non-uniqueness of…
Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. Various tools have been developed over the centuries to discover and study the various patterns in the sequence of…
A commonly used characteristic of statistical dependence of adjacency relations in real networks, the clustering coefficient, evaluates chances that two neighbours of a given vertex are adjacent. An extension is obtained by considering…