Related papers: A star based model for the eigenvalue power law of…
We compare the spectrum and the localisation properties of the eigenmodes of the Laplacian and the adjacency matrix of 2D random geometric graphs, using numerical diagonalization of these matrices for different system sizes and…
For a simple graph $G=(V,E)$ with eigenvalues of the adjacency matrix $\lambda_{1}\geq\lambda_{2}\geq\cdots\geq\lambda_{n}$, the energy of the graph is defined by $E(G)=\sum_{j=1}^{n}|\lambda_{j}|$. Myriads of papers have been published in…
We build up a directed network tracing links from a given integer to its divisors and analyze the properties of the Google matrix of this network. The PageRank vector of this matrix is computed numerically and it is shown that its…
An eigenvalue of the adjacency matrix of a graph is said to be \emph{main} if the all-1 vector is not orthogonal to the associated eigenspace. In this work, we approach the main eigenvalues of some graphs. The graphs with exactly two main…
The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, from the analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the…
Spectral analysis connects graph structure to the eigenvalues and eigenvectors of associated matrices. Much of spectral graph theory descends directly from spectral geometry, the study of differentiable manifolds through the spectra of…
Given a graph $M,$ path eigenvalues are eigenvalues of its path matrix. The path energy of a simple graph $M$ is equal to the sum of the absolute values of the path eigenvalues of the graph $M$ (Shikare et. al, 2018). We have discovered new…
It is well-known that the behavior of many dynamical processes running on networks is intimately related to the eigenvalue spectrum of the network. In this paper, we address the problem of inferring global information regarding the…
Let $G$ be a graph of order $n$ and $\mu$ be an adjacency eigenvalue of $G$ with multiplicity $k\geq 1$. A star complement $H$ for $\mu$ in $G$ is an induced subgraph of $G$ of order $n-k$ with no eigenvalue $\mu$, and the vertex subset…
We consider the adjacency matrix associated with a graph that describes transitions between $2^{N}$ states of the discrete Preisach memory model. This matrix can also be associated with the last-in-first-out inventory management rule. We…
A {\it star-factor} of a graph $G$ is a spanning subgraph of $G$ such that each of its component is a star. Clearly, every graph without isolated vertices has a star factor. A graph $G$ is called {\it star-uniform} if all star-factors of…
Numerous works have been proposed to generate random graphs preserving the same properties as real-life large scale networks. However, many real networks are better represented by hypergraphs. Few models for generating random hypergraphs…
For a given graph $G$, we aim to determine the possible realizable spectra for a generalized (or sometimes referred to as a weighted) Laplacian matrix associated with $G$. This new specialized inverse eigenvalue problem is considered for…
We perform an extensive investigation of the localization properties of the eigenmodes of the Laplace and adjacency matrix for one-dimensional random geometric graphs. We evaluate the density of states, the probability distribution of the…
In the practical work of websites popularization, analysis of their efficiency and downloading it is of key importance to take into account web-ratings data. The main indicators of website traffic include the number of unique hosts from…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the network's adjacency matrix provides an understanding of the origins of occurrence of high multiplicities in the networks…
The extreme eigenvalues of adjacency matrices are important indicators on the influences of topological structures to collective dynamical behavior of complex networks. Recent findings on the ensemble averageability of the extreme…
Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet…