Related papers: Critical phenomena on heterogeneous small-world ne…
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…
Recent results from statistical physics show that large classes of complex networks, both man-made and of natural origin, are characterized by high clustering properties yet strikingly short path lengths between pairs of nodes. This class…
Recently, the concept of geometric renormalization group provides a good approach for studying the structural symmetry and functional invariance of complex networks. Along this line, we systematically investigate the finite-size scaling of…
The possibility to identify the nature (e.g. random or scale free) of complex networks while performing respective random walks is investigated with respect to autonomous agents based on Bayesian decision theory and humans navigating…
Robust control theory has been successfully applied to numerous real-world problems using a small set of devices called {\it controllers}. However, the real systems represented by networks contain unreliable components and modern robust…
A minimal model for self-organized critical percolation on directed graphs with activating and de-activating links is studied. Unlike classical self-organized criticality, the variables that determine criticality are separated from the…
We study a cascading edge failure mechanism on a connected random graph with a prescribed degree sequence, sampled using the configuration model. This mechanism prescribes that every edge failure puts an additional strain on the remaining…
Standard Random Boolean Networks display an order-disorder phase transition. We add to the standard Random Boolean Networks a disconnection rule which couples the control and order parameters. By this way, the system is driven to the…
We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all…
Networks with underlying metric spaces attract increasing research attention in network science, statistical physics, applied mathematics, computer science, sociology, and other fields. This attention is further amplified by the current…
We study fully synchronized states in scale-free networks of chaotic logistic maps as a function of both dynamical and topological parameters. Three different network topologies are considered: (i) random scale-free topology, (ii)…
Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…
We study the Ising model in a hierarchical small-world network by renormalization group analysis, and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges.…
We search for conditions under which a characteristic time scale for ordering dynamics towards either of two absorbing states in a finite complex network of interactions does not exist. With this aim, we study random networks and networks…
One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather…
Small-world networks, i.e. networks displaying both a high clustering coefficient and a small characteristic path length, are obliquitous in nature. Since their identification, the "small-worldness" metric, as proposed by Humphries and…
It is a mainstream idea that scale-free network would be fragile under the selective attacks. Internet is a typical scale-free network in the real world, but it never collapses under the selective attacks of computer viruses and hackers.…
We demonstrate, both analytically and numerically, that learning dynamics of neural networks is generically attracted towards a self-organized critical state. The effect can be modeled with quartic interactions between non-trainable…
Real-life networks often encounter vertex dysfunctions, which are usually followed by recoveries after appropriate maintenances. In this paper we present our research on a model of scale-free networks whose vertices are regularly removed…
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…