Related papers: Universality and non-universality in behavior of s…
Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter $q$. We obtain the topological…
Using percolation statistics we, for the first time, demonstrate the universal character of a network pattern in the real space, mass distributions resulting from nonlinear gravitational instability of initial Gaussian fluctuations.…
Networks growing according to the rule that every new node has a probability p_k of being attached to k preexisting nodes, have a universal phase diagram and exhibit power law decays of the distribution of cluster sizes in the…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…
In usual scale-free networks of Barabasi-Albert type, a newly added node selects randomly m neighbors from the already existing network nodes, proportionally to the number of links these had before. Then the number N(k) of nodes with k…
Universality is a cornerstone of theories of critical phenomena. It is well understood in most systems especially in the thermodynamic limit. Finite-size systems present additional challenges. Even in low dimensions, universality of the…
Universality is one of the key concepts in understanding critical phenomena. However, for interacting inhomogeneous systems described by complex networks a clear understanding of the relevant parameters for universality is still missing.…
Evidence of critical dynamics has been recently found in both experiments and models of large scale brain dynamics. The understanding of the nature and features of such critical regime is hampered by the relatively small size of the…
Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the…
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…
A growing body of evidence suggests that the structure of mitochondrial networks is poised near criticality, an intermediate regime lying in between order and disorder. Such description fits well with the idea that biological systems, in…
We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-\delta}$ in addition to nearest neighbour connections. This system has been shown to exhibit…
Clustering and degree correlations are ubiquitous in real-world complex networks. Yet, understanding their role in critical phenomena remains a challenge for theoretical studies. Here, we provide the exact solution of site percolation in a…
Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point.…
We investigate the structural organization of the point-to-point electric, diffusive or hydraulic transport in complex scale-free networks. The random choice of two nodes, a source and a drain, to which a potential difference is applied,…
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…
We study numerically a model of nonequilibrium networks where nodes and links are added at each time step with aging of nodes and connectivity- and age-dependent attachment of links. By varying the effects of age in the attachment…
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…
Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its…
The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links, the average eccentricity and…