Related papers: Long-range connections and mixed diffusion in frac…

Small world models are networks consisting of many local links and fewer long range 'shortcuts', used to model networks with a high degree of local clustering but relatively small diameter. Here, we concern ourselves with the distribution…

We analyze the degree distribution's cut-off in finite size scale-free networks. We show that the cut-off behavior with the number of vertices $N$ is ruled by the topological constraints induced by the connectivity structure of the network.…

The human brain has been studied at multiple scales, from neurons, circuits, areas with well defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed…

Non-equilibrium diffusive systems are known to exhibit long-range correlations, which decay like the inverse 1/L of the system size L in one dimension. Here, taking the example of the ABC model, we show that this size dependence becomes…

We explore the concepts of self-similarity, dimensionality, and (multi)scaling in a new family of recursive scale-free nets that yield themselves to exact analysis through renormalization techniques. All nets in this family are self-similar…

The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools…

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…

Complex networks have been studied extensively due to their relevance to many real systems as diverse as the World-Wide-Web (WWW), the Internet, energy landscapes, biological and social networks…

Biological systems, from a cell to the human brain, are inherently complex. A powerful representation of such systems, described by an intricate web of relationships across multiple scales, is provided by complex networks. Recently, several…

In their recent work "Scale-free networks are rare", Broido and Clauset address the problem of the analysis of degree distributions in networks to classify them as scale-free at different strengths of "scale-freeness." Over the last two…

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…

In this work we study diffusion in networks with community structure. We first replicate and extend work on networks with non-overlapping community structure. We then study diffusion on network models that have overlapping community…

We present a model for disordered 3D fiber networks to study their linear and nonlinear elasticity over a wide range of network densities and fiber lengths. In contrast to previous 2D models, these 3D networks with binary cross-links are…

Cross-correlations in the activity in neural networks are commonly used to characterize their dynamical states and their anatomical and functional organizations. Yet, how these latter network features affect the spatiotemporal structure of…

Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as…

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 -…

Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular,…

Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the…

Complex networks describe a wide range of systems in nature and society. Frequently cited examples include Internet, WWW, a network of chemicals linked by chemical reactions, social relationship networks, citation networks, etc. The…

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…