Related papers: Organization of complex networks without multiple …
In this study, we performed comprehensive morphological investigations of the spontaneous formations of effective network structures among elements in coupled logistic maps, specifically with a delayed connection change. Our proposed model…
1. Basic constructions. 2. Equilibrium and nonequilibrium networks. 3. Equilibrium uncorrelated networks. 4. Nonequilibrium nongrowing scale-free nets. 5. Types of correlations. 6. When pair correlations are important. 7. When loops are…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
The rapidly developing theory of complex networks indicates that real networks are not random, but have a highly robust large-scale architecture, governed by strict organizational principles. Here, we focus on the properties of biological…
Discoveries of the scale-free and small-world features are reported on a network constructed from the seismic data. It is shown that the connectivity distribution decays as a power law, and the value of the degrees of separation, i.e., the…
The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in…
Complex networks are made up of vertices and edges. The latter connect the vertices. There are several ways to measure the importance of the vertices, e.g., by counting the number of edges that start or end at each vertex, or by using the…
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…
Given a finite set T of maps on a finite ring R, we look at the finite simple graph G=(V,E) with vertex set V=R and edge set E={(a,b) | exists t in T, b=t(a), b not equal to a}. An example is when R=Z_n and T consists of a finite set of…
In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean…
Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
A model of an evolving network of interacting molecular species is shown to exhibit repeated rounds of crashes in which several species get rapidly depopulated, followed by recoveries. The network inevitably self-organizes into an…
We propose and study a model of traffic in communication networks. The underlying network has a structure that is tunable between a scale-free growing network with preferential attachments and a random growing network. To model realistic…
Social networks are organized into communities with dense internal connections, giving rise to high values of the clustering coefficient. In addition, these networks have been observed to be assortative, i.e. highly connected vertices tend…
Core-periphery detection aims to separate the nodes of a complex network into two subsets: a core that is densely connected to the entire network and a periphery that is densely connected to the core but sparsely connected internally. The…
We propose a novel measure to assess the presence of meso-scale structures in complex networks. This measure is based on the identification of regular patterns in the adjacency matrix of the network, and on the calculation of the quantity…
We derive the finite size dependence of the clustering coefficient of scale-free random graphs generated by the configuration model with degree distribution exponent $2<\gamma<3$. Degree heterogeneity increases the presence of triangles in…
The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable…
Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include…