相关论文: Asymptotics of the spectral radius for directed Ch…
In graph analyses, directed edges are often approximated to undirected ones so that the adjacency matrices may be symmetric. However, such simplification has not been thoroughly verified. In this study, we investigate how directedness…
PageRank has numerous applications in information retrieval, reputation systems, machine learning, and graph partitioning. In this paper, we study PageRank in undirected random graphs with an expansion property. The Chung-Lu random graph is…
Stochastic network influences complicate graph filter design by producing uncertainty in network iteration matrix eigenvalues, the points at which the graph filter response is defined. While joint statistics for the eigenvalues typically…
We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…
We consider the adjacency matrices of sparse random graphs from the Chung-Lu model, where edges are added independently between the $N$ vertices with varying probabilities $p_{ij}$. The rank of the matrix $(p_{ij})$ is some fixed positive…
It has been shown that the adjacency eigenspace of a network contains key information of its underlying structure. However, there has been no study on spectral analysis of the adjacency matrices of directed signed graphs. In this paper, we…
Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific…
Random matrix theory has played an important role in recent work on statistical network analysis. In this paper, we review recent results on regimes of concentration of random graphs around their expectation, showing that dense graphs…
Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their…
Important problems in wireless networks can often be solved by computing fixed points of standard or contractive interference mappings, and the conventional fixed point algorithm is widely used for this purpose. Knowing that the mapping…
Random graph models are a recurring tool-of-the-trade for studying network structural properties and benchmarking community detection and other network algorithms. Moreover, they serve as test-bed generators for studying diffusion and…
In distributed optimization or Nash-equilibrium seeking over directed graphs, it is crucial to find a matrix norm under which the disagreement of individual agents' states contracts. In existing results, the matrix norm is usually defined…
We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks…
In this paper, we give upper and lower bounds for the spectral radius of a nonnegative irreducible matrix and characterize the equality cases. These bounds theoretically improve and generalize some known results of Duan et al.[X. Duan, B.…
Random graph models play a central role in network analysis. The Chung-Lu model, which connects nodes based on their expected degrees is of particular interest. It is widely used to generate null-graph models with expected degree sequences…
Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term…
In this paper, we analyze the limiting spectral distribution of the adjacency matrix of a random graph ensemble, proposed by Chung and Lu, in which a given expected degree sequence $\overline{w}_n^{^{T}} = (w^{(n)}_1,\ldots,w^{(n)}_n)$ is…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
PageRank has numerous applications in information retrieval, reputation systems, machine learning, and graph partitioning.In this paper, we study PageRank in undirected random graphs with expansion property. The Chung-Lu random graph…
We establish an Expander Mixing Lemma for directed graphs in terms of the eigenvalues of an associated asymmetric transition probability matrix, extending the classical spectral inequality to the asymmetric setting. As an application, we…