Related papers: Eigenvector localization in real networks and its …
We study spectra of directed networks with inhibitory and excitatory couplings. We investigate in particular eigenvector localization properties of various model networks for different value of correlation among their entries. Spectra of…
Although the spectral properties of random graphs have been a long-standing focus of network theory, the properties of right eigenvectors of directed graphs have so far eluded an exact analytic treatment. We present a general theory for the…
The nonbacktracking matrix, and the related nonbacktracking centrality (NBC) play a crucial role in models of percolation-type processes on networks, such as non-recurrent epidemics. Here we study the localization of NBC in infinite sparse…
Localization behaviours of Laplacian eigenvectors of complex networks provide understanding to various dynamical phenomena on the corresponding complex systems. We numerically investigate role of hyperedges in driving eigenvector…
We analyse the eigenvectors of the adjacency matrix of a random inhomogeneous graph constructed from a specified degree sequence. We assume that the empirical degree sequence has bounded mean and variance. We show that near the edges of the…
We study how the behavior of viral spreading processes is influenced by local structural properties of the network over which they propagate. For a wide variety of spreading processes, the largest eigenvalue of the adjacency matrix of the…
We consider highly heterogeneous random networks with symmetric interactions in the limit of high connectivity. A key feature of this system is that the spectral density of the corresponding ensemble exhibits a divergence within the bulk.…
We investigate gene interaction networks in various cancer cells by spectral analysis of the adjacency matrices. We observe localization of the networks on hub genes which have extraordinarily many links. The eigenvector centralities take…
Random graphs defined by an occurrence probability that is invariant under node aggregation have been identified recently in the context of network renormalization. The invariance property requires that edges are drawn with a specific…
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…
Euclidean random matrices arise in a wide range of physical systems where interactions are determined by spatial configurations, including disordered media and cooperative phenomena in atomic ensembles. Unlike classical random matrix…
Many real-world complex systems have small-world topology characterized by the high clustering of nodes and short path lengths.It is well-known that higher clustering drives localization while shorter path length supports delocalization of…
We present a novel approach for computing a variant of eigenvector centrality for multilayer networks with inter-layer constraints on node importance. Specifically, we consider a multilayer network defined by multiple edge-weighted,…
Using exact numerical diagonalization, we investigate localization in two classes of random matrices corresponding to random graphs. The first class comprises the adjacency matrices of Erdos-Renyi (ER) random graphs. The second one…
This paper develops the exact linear relationship between the leading eigenvector of the unnormalized modularity matrix and the eigenvectors of the adjacency matrix. We propose a method for approximating the leading eigenvector of the…
With great theoretical and practical significance, identifying the node spreading influence of complex network is one of the most promising domains. So far, various topology-based centrality measures have been proposed to identify the node…
The article considers an inhomogeneous Erd\H{o}s-R\"enyi random graph on $\{1,\ldots, N\}$, where an edge is placed between vertices $i$ and $j$ with probability $\varepsilon_N f(i/N,j/N)$, for $i\le j$, the choice being made independent…
The principal ratio of a graph is the ratio of the greatest and least entry of its principal eigenvector. Since the principal ratio compares the extreme values of the principal eigenvector it is sensitive to outliers. This can be…
Link prediction is a fundamental challenge in network science. Among various methods, similarity-based algorithms are popular for their simplicity, interpretability, high efficiency and good performance. In this paper, we show that the most…
Social networks are discrete systems with a large amount of heterogeneity among nodes (individuals). Measures of centrality aim at a quantification of nodes' importance for structure and function. Here we ask to which extent the most…