Related papers: Spectral Properties of the Threshold Network Model
The spectrum of the adjacency matrix plays several important roles in the mathematical theory of networks and in network data analysis, for example in percolation theory, community detection, centrality measures, and the theory of dynamical…
We study the spectral properties of the process of explosive percolation. In particular, we explore how the maximum eigenvalue of the adjacency matrix of a network which governs the spreading efficiency evolves as the density of connection…
Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are…
We study the diversity of complex spatio-temporal patterns of random synchronous asymmetric neural networks (RSANNs). Specifically, we investigate the impact of noisy thresholds on network performance and find that there is a narrow and…
We derive the probability that a randomly chosen NL-node over $S$ gets localized as a function of a variety of parameters. Then, we derive the probability that the whole network of NL-nodes over $S$ gets localized. In connection with the…
Epidemiological contact network models have emerged as an important tool in understanding and predicting the spread of infectious disease, due to their capacity to engage individual heterogeneity that may underlie essential dynamics of a…
We constructs a new network by superposition of hexahedron , which are scale-free, highly sparse,disassortative ,and maximal planar graphs. The network degree distribution, agglomeration coefficient and degree of correlation are computed…
We introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network. Spectral graph theory is used to quantify how close to bipartite a network is and the extent to which…
The spread of a disease, a computer virus or information is discussed in a directed complex network. We are concerned with a steady state of the spread for the SIR and SIS dynamic models. In a scale-free directed network it is shown that…
We have developed a linearization method to investigate the subthreshold oscillatory behaviors in nonlinear autonomous systems. By considering firstly the neuronal system as an example, we show that this theoretical approach can predict…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
Our talk at Lisbon SAMP conference was based mainly on our recent results (published in Comm. Math. Phys.) on small diameter asymptotics for solutions of the Helmgoltz equation in networks of thin fibers. The present paper contains a…
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…
In 2009, two different groups independently explored the behavior of random threshold graphs. Here, we extend their techniques to find the distribution of other properties, including matching number, degeneracy, and length of the longest…
A complex network is said to show topological isotropy if the topological structure around a particular node looks the same in all directions of the whole network. Topologically anisotropic networks are those where the local neighborhood…
We imitate the spectrum character of one-dimensional disorder system with our new rain model. It has been shown that the transmission spectrum can be approximately characterized by the model, which include some coupled lorentzian…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
The transmission or reception of packets passing between computers can be represented in terms of time-stamped events and the resulting activity understood in terms of point-processes. Interestingly, in the disparate domain of neuroscience,…
In this paper, we analyse spectral properties of Seidel matrix (denoted by $S$) of connected threshold graphs. We compute the characteristic polynomial and determinant of Seidel matrix of threshold graphs. We derive formulas for the…
In this paper we introduce a model which provides a new approach to the phenomenon of stochastic resonance. It is based on the study of the properties of the stationary distribution of the underlying stochastic process. We derive the…