Related papers: Offdiagonal Complexity: A computationally quick co…

A prominent tool in many problems involving metric spaces is a notion of randomized low-diameter decomposition. Loosely speaking, $\beta$-decomposition refers to a probability distribution over partitions of the metric into sets of low…

Datasets from several domains, such as life-sciences, semantic web, machine learning, natural language processing, etc. are naturally structured as acyclic graphs. These datasets, particularly those in bio-informatics and computational…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…

In this work we investigate the problem of estimating the percolation centrality of every vertex in a graph. This centrality measure quantifies the importance of each vertex in a graph going through a contagious process. It is an open…

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…

Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a very complicated structure that is poorly understood and determined…

Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand the information interchange in networks of dynamical systems, and uncover the interplay between…

In this paper we propose a distributed algorithm for the estimation and control of the connectivity of ad-hoc networks in the presence of a random topology. First, given a generic random graph, we introduce a novel stochastic power…

A drawback of the classic approach for complexity analysis of distributed graph problems is that it mostly informs about the complexity of notorious classes of ``worst case'' graphs. Algorithms that are used to prove a tight (existential)…

The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…

The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding…

We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…

The statistical modeling of random networks has been widely used to uncover interaction mechanisms in complex systems and to predict unobserved links in real-world networks. In many applications, network connections are collected via…

We constructs a new network by superposition of hexahedron , which are scale-free, highly sparse,disassortative ,and maximal planar graphs. The network degree distribution, agglomeration coefficient and degree of correlation are computed…

One of the central challenges facing modern neuroscience is to explain the ability of the nervous system to coherently integrate information across distinct functional modules in the absence of a central executive. To this end Tononi et al.…

We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…

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…

In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…

We explore the relation between the topological relevance of a node in a complex network and the individual dynamics it exhibits. When the system is weakly coupled, the effect of the coupling strength against the dynamical complexity of the…

We suggest an approach to study hierarchy, especially hidden one, of complex networks based on the analysis of their vulnerability. Two quantities are proposed as a measure of network hierarchy. The first one is the system vulnerability V.…