Related papers: Towards fractal origins of the community structure…

We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like structure, which is mathematically described by the scale-invariant equation for the masses of the boxes…

We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the…

The fractal nature of complex networks has received a great deal of research interest in the last two decades. Similarly to geometric fractals, the fractality of networks can also be defined with the so-called box-covering method. A network…

Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…

Many social and biological networks consist of communities - groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable interest in designing algorithms for detecting…

Complex networks from such different fields as biology, technology or sociology share similar organization principles. The possibility of a unique growth mechanism promises to uncover universal origins of collective behaviour. In…

Social structures emerge as a result of individuals managing a variety of different of social relationships. Societies can be represented as highly structured dynamic multiplex networks. Here we study the dynamical origins of the specific…

In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension.…

This paper presents a versatile model for generating fractal complex networks that closely mirror the properties of real-world systems. By combining features of reverse renormalization and evolving network models, the proposed approach…

Many real-world complex systems such as social, biological, information as well as technological systems results of a decentralized and unplanned evolution which leads to a common structuration. Irrespective of their origin, these so-called…

Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects…

In this paper we study self-similar and fractal networks from the combinatorial perspective. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to…

We draw attention to a clear dichotomy between small-world networks exhibiting exponential neighborhood growth, and fractal-like networks where neighborhoods grow according to a power law. This distinction is observed in a number of…

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…

Two aspects of fractal networks are considered: the community structure and the class structure, where classes of nodes appear as a consequence of a local symmetry of nodes. The analysed systems are the networks constructed for two selected…

Although the community structure organization is one of the most important characteristics of real-world networks, the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for…

We propose a dynamical model in which a network structure evolves in a self-organized critical (SOC) manner and explain a possible origin of the emergence of fractal and small-world networks. Our model combines a network growth and its…

In this article, we present a novel box-covering algorithm for analyzing the fractal properties of complex networks. Unlike traditional algorithms that impose a predetermined box size, our approach assigns nodes to boxes identified by their…

It is widely believed that fractality of complex networks origins from hub repulsion behaviors (anticorrelation or disassortativity), which means large degree nodes tend to connect with small degree nodes. This hypothesis was demonstrated…

Analysis and modeling of networked objects are fundamental pieces of modern data mining. Most real-world networks, from biological to social ones, are known to have common structural properties. These properties allow us to model the growth…