Related papers: Superelliptical laws for complex networks
We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the…
In this paper we investigate phenomena of spontaneous emergence or purposeful formation of highly organized structures in networks of related agents. We show that the formation of large organized structures requires exponentially large, in…
Networked systems that occur in various domains, such as the power grid, the brain, and opinion networks, are known to obey conservation laws. For instance, electric networks obey Kirchoff's laws, and social networks display opinion…
Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…
We investigate the dynamics of two models of biological networks with purely suppressive interactions between the units; species interacting via niche competition and neurons via inhibitory synaptic coupling. In both of these cases,…
The principle of similarity, or homophily, is often used to explain patterns observed in complex networks such as transitivity and the abundance of triangles (3-cycles). However, many phenomena from division of labor to protein-protein…
We analyze critical phenomena on networks generated as the union of hidden variables models (networks with any desired degree sequence) with arbitrary graphs. The resulting networks are general small-worlds similar to those a` la Watts and…
We introduce evolving networks where new vertices preferentially connect to the more central parts of a network. This makes such networks compact. Finite networks grown under the preferential compactness mechanism have complex…
Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of…
Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered…
We study the properties of metrics aimed at the characterization of grid-like ordering in complex networks. These metrics are based on the global and local behavior of cycles of order four, which are the minimal structures able to identify…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
Many complex systems have natural representations as multi-layer networks. While these formulations retain more information than standard single-layer network models, there is not yet a fully developed theory for computing network metrics…
Since E.P.Wigner (1958) established his famous semicircle law, lots of attention has been paid by physicists, probabilists and statisticians to study the asymptotic properties of the largest eigenvalues for random matrices. Bai and Yin…
"Every object that biology studies is a system of systems." (Fran\c{c}ois Jacob, 1974). Most networks feature intricate architectures originating from tinkering, a repetitive use of existing components where structures are not invented but…
Multiplex networks are complex graph structures in which a set of entities are connected to each other via multiple types of relations, each relation representing a distinct layer. Such graphs are used to investigate many complex…
Complex networks have attracted increasing interest from various fields of science. It has been demonstrated that each complex network model presents specific topological structures which characterize its connectivity and dynamics. Complex…
The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional…
Most complex systems are nonlinear, relying on emergent behavior from interacting subsystems, often characterized by oscillatory dynamics. Collective oscillatory behavior is essential for the proper functioning of many real world systems.…