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In a recent work [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], Schneider et al. proposed a new measure for network robustness and investigated optimal networks with respect to this quantity. For networks with a power-law degree…
Identifying the node spreading influence in networks is an important task to optimally use the network structure and ensure the more efficient spreading in information. In this paper, by taking into account the shortest distance between a…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
Complex networks characterized by global transport processes rely on the presence of directed paths from input to output nodes and edges, which organize in characteristic linked components. The analysis of such network-spanning structures…
The analysis of the dynamics on complex networks is closely connected to structural features of the networks. Features like, for instance, graph-cores and node degrees have been studied ubiquitously. Here we introduce the D-spectrum of a…
Complex networks are characterized by several topological properties: degree distribution, clustering coefficient, average shortest path length, etc. Using a simple model to generate scale-free networks embedded on geographical space, we…
Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally…
With the evolution of social networks, the network structure shows dynamic nature in which nodes and edges appear as well as disappear for various reasons. The role of a node in the network is presented as the number of interactions it has…
A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…
Both empirical and theoretical investigations of scale-free network models have found that large degrees in a network exert an outsized impact on its structure. However, the tools used to infer the tail behavior of degree distributions in…
A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges. The network structure,…
The concept of 'complexity' plays a central role in complex network science. Traditionally, this term has been taken to express heterogeneity of the node degrees of a therefore complex network. However, given that the degree distribution is…
We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly…
Social network structure is very important for understanding human information diffusing, cooperating and competing patterns. It can bring us with some deep insights about how people affect each other. As a part of complex networks, social…
Networks are fundamental to the study of complex systems, ranging from social contacts, message transactions, to biological regulations and economical networks. In many realistic applications, these networks may vary over time. Modeling and…
We give exact relations for certain types of the hierarchic fractal structures. In the blatant distinction from regular networks of the "small world" (SW) topology [1], regular fractal networks manifests the logarithmic dependence of the…
Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…
The design of robust supply and distribution systems is one of the fundamental challenges at the interface of network science and logistics. Given the multitude of performance criteria, real-world constraints, and external influences acting…
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…
Spreading of either information or matter can often be treated as a network problem. It can be of great importance to be able to estimate the likelihood that spreading through a network reaches essentially the entire network while still not…