Related papers: Some properties of hierarchic regular networks (a …

Hierarchical networks actually have many applications in the real world. Firstly, we propose a new class of hierarchical networks with scale-free and fractal structure, which are the networks with triangles compared to traditional…

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…

The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…

In this paper, firstly, we study analytically the topological features of a family of hierarchical lattices (HLs) from the view point of complex networks. We derive some basic properties of HLs controlled by a parameter $q$. Our results…

Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the…

Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. We show that these two features are the consequence of a hierarchical organization, implying that small…

The Erdos-Renyi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to…

Two new classes of networks are introduced that resemble small-world properties. These networks are recursively constructed but retain a fixed, regular degree. They consist of a one-dimensional lattice backbone overlayed by a hierarchical…

Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…

One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of…

Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…

We explore a new variant of Small-World Networks (SWNs), in which an additional parameter ($r$) sets the length scale over which shortcuts are uniformly distributed. When $r=0$ we have an ordered network, whereas $r=1$ corresponds to the…

We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…

Many real-world complex networks simultaneously exhibit topological features of scale-free behaviour and hierarchical organization. In this regard, deterministic scale-free [A.-L. Barab\'asi \etal, Physica A, 299, 3 (2001)] and…

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…

In recent years, the theory and application of complex networks have been quickly developing in a markable way due to the increasing amount of data from real systems and to the fruitful application of powerful methods used in statistical…

Hierarchical networks are attracting a renewal interest for modelling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean-field limitations. Here we consider the…

Hierarchically structured materials, which possess distinct features on different length scales, are ubiquitous in nature and engineering. In many cases, one structural level may be ordered while another structural level may be disordered.…

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…

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…