Related papers: Spectral methods and cluster structure in correlat…

The measured correlations of financial time series in subsequent epochs change considerably as a function of time. When studying the whole correlation matrices, quasi-stationary patterns, referred to as market states, are seen by applying…

The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…

This paper analyzes correlations in patterns of trading of different members of the London Stock Exchange. The collection of strategies associated with a member institution is defined by the sequence of signs of net volume traded by that…

Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density…

Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…

Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency…

One of the most important challenges in network science is to quantify the information encoded in complex network structures. Disentangling randomness from organizational principles is even more demanding when networks have a multiplex…

Eigenvalue-based detectors are considered as an important method of spectrum sensing since they do not require the information about the primary user (PU) signal. In this paper we propose a method to improve the performance of the…

We describe centralities in temporal networks using a supracentrality framework to study centrality trajectories, which characterize how the importances of nodes change in time. We study supracentrality generalizations of eigenvector-based…

Training of neural networks can be reformulated in spectral space, by allowing eigenvalues and eigenvectors of the network to act as target of the optimization instead of the individual weights. Working in this setting, we show that the…

This paper characterizes the difficulty of estimating a network's eigenvector centrality only from data on the nodes, i.e., with no information about the topology of the network. We model this nodal data as graph signals generated by…

McKay proved that the limiting spectral measures of the ensembles of $d$-regular graphs with $N$ vertices converge to Kesten's measure as $N\to\infty$. In this paper we explore the case of weighted graphs. More precisely, given a large…

Spectral clustering is widely used to partition graphs into distinct modules or communities. Existing methods for spectral clustering use the eigenvalues and eigenvectors of the graph Laplacian, an operator that is closely associated with…

Financial stock return correlations have been analyzed through the lens of random matrix theory to differentiate the underlying signal from spurious correlations. The continuous spectrum of the eigenvalue distribution derived from the stock…

Communities commonly overlap in real-world networks. This is a motivation to develop overlapping community detection methods, because methods for non-overlapping communities may not perform well. However, deterioration mechanism of the…

Motivated by community detection, we characterise the spectrum of the non-backtracking matrix $B$ in the Degree-Corrected Stochastic Block Model. Specifically, we consider a random graph on $n$ vertices partitioned into two equal-sized…

Spectral clustering is a leading and popular technique in unsupervised data analysis. Two of its major limitations are scalability and generalization of the spectral embedding (i.e., out-of-sample-extension). In this paper we introduce a…

Among community detection methods, spectral clustering enjoys two desirable properties: computational efficiency and theoretical guarantees of consistency. Most studies of spectral clustering consider only the edges of a network as input to…

This paper introduces a novel framework that combines traditional centrality measures with eigenvalue spectra and diffusion processes for a more comprehensive analysis of complex networks. While centrality measures such as degree,…

We investigate eigenvalues of many-body systems interacting by two-body forces as well as those of random matrices. We find a strong linear correlation between eigenvalues and diagonal matrix elements if both of them are sorted from the…