Related papers: A star based model for the eigenvalue power law of…
We consider the extremal values of the stationary distribution of sparse directed random graphs with given degree sequences and their relation to the extremal values of the in-degree sequence. The graphs are generated by the directed…
We propose a theoretical framework to study the eigenvalue spectra of the controllability Gramian of systems with random state matrices, such as networked systems with a random graph structure. Using random matrix theory, we provide…
Preferential attachment models are a common class of graph models which have been used to explain why power-law distributions appear in the degree sequences of real network data. One of the things they lack, however, is higher-order network…
In this paper we study two classes of graphs, the (m,k)-stars and l-dependent graphs, investigating the relation between spectrum characteristics and graph structure: conditions on the topology and edge weights are given in order to get…
In this paper, we describe some recent spectral Moore theorems related to determining the maximum order of a connected graph of given valency and second eigenvalue. We show how these spectral Moore theorems have applications in Alon-Boppana…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
Degree correlation plays a crucial role in studying network structures; however, its varied forms pose challenges to understanding its impact on network dynamics. This study devised a method that uses eigenvalue decomposition to…
Eigenvector centrality is a standard network analysis tool for determining the importance of (or ranking of) entities in a connected system that is represented by a graph. However, many complex systems and datasets have natural multi-way…
We derive qualitative relationships about the informational relevance of variables in graphical decision models based on a consideration of the topology of the models. Specifically, we identify dominance relations for the expected value of…
We find large deviations rates for consensus-based distributed inference for directed networks. When the topology is deterministic, we establish the large deviations principle and find exactly the corresponding rate function, equal at all…
Consider an eigenvector of the adjacency matrix of a G(n, p) graph. A nodal domain is a connected component of the set of vertices where this eigenvector has a constant sign. It is known that with high probability, there are exactly two…
In this paper, we propose a model enabling the creation of a social graph corresponding to real society. The procedure uses data describing the real social relations in the community, like marital status or number of kids. Results show the…
This paper describes a model for power distribution network, which is hten utilized for eigenvalue behavior distribution analysis. We utilized the compensation theory to model the event that occurs in the network and derived the relation…
Finding a diagonal matrix congruent to $A - cI$ for constants $c$, where $A$ is the adjacency matrix of a graph $G$ allows us to quickly tell the number of eigenvalues in a given interval. If $G$ has clique-width $k$ and a corresponding…
The PageRank algorithm enables to rank the nodes of a network through a specific eigenvector of the Google matrix, using a damping parameter $\alpha \in ]0,1[$. Using extensive numerical simulations of large web networks, with a special…
A theory of orientation on gain graphs (voltage graphs) is developed to generalize the notion of orientation on graphs and signed graphs. Using this orientation scheme, the line graph of a gain graph is studied. For a particular family of…
We study the eigenvectors and eigenvalues of random matrices with iid entries. Let $N$ be a random matrix with iid entries which have symmetric distribution. For each unit eigenvector $\mathbf{v}$ of $N$ our main results provide a small…
A complex unit gain graph is a simple graph in which each orientation of an edge is given a complex number with modulus 1 and its inverse is assigned to the opposite orientation of the edge. In this article, first we establish bounds for…
Eigenvalue interlacing is a versatile technique for deriving results in algebraic combinatorics. In particular, it has been successfully used for proving a number of results about the relation between the (adjacency matrix or Laplacian)…
In this article, we explicitly derive the limiting degree distribution of the shortest path tree from a single source on various random network models with edge weights. We determine the asymptotics of the degree distribution for large…