Related papers: Local structure of directed networks
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are…
We reveal a hierarchical, multilayer organization of finite components -- i.e., tendrils and tubes -- around the giant connected components in directed networks and propose efficient algorithms allowing one to uncover the entire…
We characterize the distributions of short cycles in a large metabolic network previously shown to have small world characteristics and a power law degree distribution. Compared with three classes of random networks, including Erdoes-Renyi…
The behaviour of complex networks under failure or attack depends strongly on the specific scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure but appear to be especially vulnerable…
From the perspective of network analysis, the ubiquitous networks are comprised of regular and irregular components, which makes uncovering the complexity of network structures to be a fundamental challenge. Exploring the regular…
Directionality is a fundamental feature of network connections. Most structural brain networks are intrinsically directed because of the nature of chemical synapses, which comprise most neuronal connections. Due to limitations of…
For decades, complex networks, such as social networks, biological networks, chemical networks, technological networks, have been used to study the evolution and dynamics of different kinds of complex systems. These complex systems can be…
The study of dynamical systems on networks, describing complex interactive processes, provides insight into how network structure affects global behaviour. Yet many methods for network dynamics fail to cope with large or partially-known…
Although the analysis of loops is not so much because of the complications, it has already been found that heuristically enhancing loops decreases the variance of degree distributions for improving the robustness of connectivity. While many…
Synchronization phenomena on networks have attracted much attention in studies of neural, social, economic, and biological systems, yet we still lack a systematic understanding of how relative synchronizability relates to underlying network…
Directed cycles form the fundamental motifs in natural, social and artificial networks, yet their distinct computational roles remain under-explored, particularly in the context of higher-order structure and function. In this work, we…
Networks are widely used to represent interaction pattern among the components in complex systems. Structures of real networks from differ- ent domains may vary quite significantly. Since there is an interplay be- tween network architecture…
Complex networks as the World Wide Web, the web of human sexual contacts or criminal networks often do not have an engineered architecture but instead are self-organized by the actions of a large number of individuals. From these local…
Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…
We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks…
Modular structure is ubiquitous among complex networks. We note that most such systems are subject to multiple structural and functional constraints, e.g., minimizing the average path length and the total number of links, while maximizing…
Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry are the geometry of latent spaces underlying many networks, and…
We consider a network of identical, first-order linear systems, and investigate how replacing a subset of the systems composing the network with higher-order ones, either taken to be generic or specifically designed, may affect its…
Motivated by the abundance of directed synaptic couplings in a real biological neuronal network, we investigate the synchronization behavior of the Hodgkin-Huxley model in a directed network. We start from the standard model of the…
Over the last two decades, network theory has shown to be a fruitful paradigm in understanding the organization and functioning of real-world complex systems. One technique helpful to this endeavor is identifying functionally influential…