Related papers: Full Connectivity: Corners, edges and faces
The task of manipulating correlated random variables in a distributed setting has received attention in the fields of both Information Theory and Computer Science. Often shared correlations can be converted, using a little amount of…
The paper develops a general framework for constrained clustering which is based on the close connection of geometric clustering and diagrams. Various new structural and algorithmic results are proved (and known results generalized and…
Many of the structural characteristics of a network depend on the connectivity with and within the hubs. These dependencies can be related to the degree of a node and the number of links that a node shares with nodes of higher degree. In…
We study the emergence of coherence in complex networks of mutually coupled non-identical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, on the isolated dynamics of the elements and the…
We study limits of the largest connected components (viewed as metric spaces) obtained by critical percolation on uniformly chosen graphs and configuration models with heavy-tailed degrees. For rank-one inhomogeneous random graphs, such…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
We consider the density at a point z = x + i y of critical percolation clusters that touch the left [P_L(z)], right [P_R(z)], or both [P_{LR}(z)] sides of a rectangular system, with open boundary conditions on the top and bottom. The ratio…
Random hypergraph is a broad concept used to describe probability distributions over hypergraphs, which are mathematical structures with applications in various fields, e.g., complex systems in physics, computer science, social sciences,…
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…
In many networks such as transportation or communication networks, distance is certainly a relevant parameter. In addition, real-world examples suggest that when long-range links are existing, they usually connect to hubs-the well connected…
We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for…
Ad-hoc networks are often deployed in regions with complicated boundaries. We show that if the boundary is modeled as a fractal, a network requiring line of sight connections has the counterintuitive property that increasing the number of…
We conjecture an exact form for an universal ratio of four-point cluster connectivities in the critical two-dimensional $Q$-color Potts model. We also provide analogous results for the limit $Q\rightarrow 1$ that corresponds to percolation…
Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…
We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also…
We find conditions for the connectivity of inhomogeneous random graphs with intermediate density. Our results generalize the classical result for G(n, p), when p = c log n/n. We draw n independent points X_i from a general distribution on a…
The threshold network model is a type of finite random graphs. In this paper, we introduce a generalized threshold network model. A pair of vertices with random weights is connected by an edge when real-valued functions of the pair of…
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…
An analytical approach to calculating bond percolation thresholds, sizes of $k$-cores, and sizes of giant connected components on structured random networks with non-zero clustering is presented. The networks are generated using a…
In the paper, we study fluctuations over several ensembles of maximum-entropy random networks. We derive several fluctuation-dissipation relations characterizing susceptibilities of different networks to changes in external fields. In the…