Related papers: Hierarchical Organization in Complex Networks
Clustering and community structure is crucial for many network systems and the related dynamic processes. It has been shown that communities are usually overlapping and hierarchical. However, previous methods investigate these two…
Recent developments in graph theoretic analysis of complex networks have led to deeper understanding of brain networks. Many complex networks show similar macroscopic behaviors despite differences in the microscopic details. Probably two…
To comprehend the hierarchical organization of large integrated systems, we introduce the hierarchical map equation, which reveals multilevel structures in networks. In this information-theoretic approach, we exploit the duality between…
A complex network is said to show topological isotropy if the topological structure around a particular node looks the same in all directions of the whole network. Topologically anisotropic networks are those where the local neighborhood…
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…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
Complex networks have abundant and extensive applications in real life. Recently, researchers have proposed a number of complex networks, in which some are deterministic and others are random. Compared with deterministic networks, random…
Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order…
A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree $k$ follows a power law, decaying like $k^{-\alpha}$, often with $2 < \alpha < 3$. However,…
Community structure is one of the key properties of complex networks and plays a crucial role in their topology and function. While an impressive amount of work has been done on the issue of community detection, very little attention has…
The characterization of large-scale structural organization of social networks is an important interdisciplinary problem. We show, by using scaling analysis and numerical computation, that the following factors are relevant for models of…
Real world networks have, for a long time, been modelled by scale-free networks, which have many sparsely connected nodes and a few highly connected ones (the hubs). However, both in society and in biology, a new structure must be…
Looking to overcome the limitations of traditional networks, the network science community has lately given much attention to the so-called higher-order networks, where group interactions are modeled alongside pairwise ones. While degree…
We study the large-scale topological and dynamical properties of real Internet maps at the autonomous system level, collected in a three years time interval. We find that the connectivity structure of the Internet presents average…
The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows to find the critical threshold and the size of the giant component. Numerical simulations…
We study a recently introduced class of scale-free networks showing a high clustering coefficient and non-trivial connectivity correlations. We find that the connectivity probability distribution strongly depends on the fine details of the…
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 mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…
It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. Although most of…
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 -…