Related papers: Survival probability of random networks
The eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior. In particular, the spectral density $\rho(\lambda)$ of this matrix reveals important network…
A particle initially in a pure state but interacting with some environment evolves into a discrete ensemble of pure states, the eigenstates of its reduced density operator, with ensemble probabilities given by the corresponding eigenvalues.…
Under what conditions is an edge present in a social network at time t likely to decay or persist by some future time t + Delta(t)? Previous research addressing this issue suggests that the network range of the people involved in the edge,…
The aim of the study was to compare the epidemic spread on static and dynamic small-world networks. The network was constructed as a 2-dimensional Watts-Strogatz model (500x500 square lattice with additional shortcuts), and the dynamics…
With a simple model, we study the evolution of random networks under attack and reconstruction. We introduce a new quality, invulnerability I(s), to describe the stability of the system. We find that the network can evolve to a stationary…
We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdos-Renyi (E-R) random graph is determined by the average degree <k>, and p(s) undergoes a…
To better understand the temporal characteristics and the lifetime of fluctuations in stochastic processes in networks, we investigated diffusive persistence in various graphs. Global diffusive persistence is defined as the fraction of…
The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios…
We analyze gene co-expression network under the random matrix theory framework. The nearest neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral…
In random matrices with independent and continuous matrix entries, the degeneracy probability of the eigenvalues is known to be zero. In this paper, random matrices including discontinuous matrix entries are analyzed in order to observe how…
We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are…
A novel route to the exponential trapping-time distribution within a solidlike state in water clusters is described. We propose a simple homogeneous network (SHN) model to investigate dynamics on the potential energy networks of water…
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…
The adiabatic connection fluctuation-dissipation theorem with the random phase approximation (RPA) has recently been applied with success to obtain correlation energies of a variety of chemical and solid state systems. The main merit of…
We introduce a minimalistic model based on dynamic node deletion and node duplication with heterodimerisation. The model is intended to capture the essential features of the evolution of protein interaction networks. We derive an exact…
We study the phase transition from the persistence phase to the extinction phase for the SIRS (susceptible/ infected/ refractory/ susceptible) model of diseases spreading on random networks. By studying temporal evolution and…
Many complex systems--from social and communication networks to biological networks and the Internet--are thought to exhibit scale-free structure. However, prevailing explanations rely on the constant addition of new nodes, an assumption…
Structure-induced features of the wave functions for the quantum systems on complex networks are discussed in this paper. For a quantum system on a network, the state corresponding to the eigenvalue close to the center of the spectrum is…
The decay rate of SIS epidemics on the complete graph $K_{N}$ is computed analytically, based on a new, algebraic method to compute the second largest eigenvalue of a stochastic three-diagonal matrix up to arbitrary precision. The latter…
Scaling laws for neural networks, in which the loss decays as a power-law in the number of parameters, data, and compute, depend fundamentally on the spectral structure of the data covariance, with power-law eigenvalue decay appearing…