Related papers: Scaling relation for earthquake networks
Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model…
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…
The Gutenberg-Richter power law distribution of earthquake sizes is one of the most famous example illustrating self-similarity. It is well-known that the Gutenberg-Richter distribution has to be modified for large seismic moments, due to…
A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…
A measure of the correlation between two earthquakes is used to link events to their aftershocks, generating a growing network structure. In this framework one can quantify whether an aftershock is close or far, from main shocks of all…
Performance of standard processes over large distributed networks typically scales with the size of the network. For example, in planar topologies where nodes communicate with their natural neighbors, the scaling factor is $O(n)$, where $n$…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
The degree distributions of many real world networks follow power-laws whose exponents tend to fall between two and three. Within the framework of the Barabasi-Albert model (BA model), we explain this empirical observation by a simple fact.…
We propose that the widely observed and universal Gutenberg-Richter relation is a mathematical consequence of the critical branching nature of earthquake process in a brittle fracture environment. These arguments, though preliminary, are…
What is the underlying mechanism leading to power-law degree distributions of many natural and artificial networks is still at issue. We consider that scale-free networks emerges from self-organizing process, and such a evolving model is…
We analyze regional earthquake energy statistics from the Southern California and Japan seismic catalogs and find scale-invariant energy distributions characterized by an exponent $\tau \simeq 1.67$. To quantify how closely scale-invariant…
Spatial distances between subsequent earthquakes in southern California exhibit scale-free statistics, with a critical exponent $\delta \approx 0.6$, as well as finite size scaling. The statistics are independent of the threshold magnitude…
Scale-free networks are characterized by a degree distribution with power-law behavior and have been shown to arise in many areas, ranging from the World Wide Web to transportation or social networks. Degree distributions of observed…
Motivated by the fact that empirical time series of earthquakes exhibit long-range correlations in space and time and the Gutenberg-Richter distribution of magnitudes, we propose a simple fault model that can account for these types of…
It is commonly believed that scale-free networks are robust to massive numbers of random node deletions. For example, Cohen et al. study scale-free networks including some which approximate the measured degree distribution of the Internet.…
Scale-free networks arise from power-law degree distributions. Due to the finite size of real-world networks, the power law inevitably has a cutoff at some maximum degree $\Delta$. We investigate the relative size of the giant component $S$…
Despite their diverse origin, networks of large real-world systems reveal a number of common properties including small-world phenomena, scale-free degree distributions and modularity. Recently, network self-similarity as a natural outcome…
Nonlinear dissipative systems in the state of self-organized criticality release energy sporadically in avalanches of all sizes, such as in earthquakes, auroral substorms, solar and stellar flares, soft gamma-ray repeaters, and pulsar…
The Asymmetric BA model extends the Barab\'asi-Albert scale-free network model by introducing a parameter $\omega$. As $\omega$ varies, the model transitions through different network structures: an extended lattice at $\omega = -1$, a…
Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like $P(k)\approx…