New Lower Bounds for the Fundamental Weight of the Principal Eigenvector in Complex Networks

We propose a method to detect nodes of relative importance, e.g. hubs, in an unknown network based on a set of measured time series. The idea is to construct a matrix characterizing the synchronization probabilities between various pairs of time series and examine the components of the principal eigenvector. We provide a heuristic argument indicating the existence of an approximate one-to-one correspondence between the components and the degrees of the nodes from which measurements are obtained. The striking finding is that such a correspondence appears to be quite robust, which holds regardless of the detailed node dynamics and of the network topology. Our computationally efficient method thus provides a general means to address the important problem of network detection, with potential applications in a number of fields.

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On the spectral radii and principal eigenvectors of uniform hypergraphs

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830917500483 ◽

2017 ◽

Vol 09 (04) ◽

pp. 1750048 ◽

Cited By ~ 1

Author(s):

Xuelian Si ◽

Xiying Yuan

Keyword(s):

Spectral Radius ◽

Lower Bounds ◽

Uniform Hypergraph ◽

Principal Eigenvector ◽

Uniform Hypergraphs ◽

Positive Eigenvector ◽

Spectral Radius Formula

Let [Formula: see text] be a connected [Formula: see text]-uniform hypergraph. The unique positive eigenvector [Formula: see text] with [Formula: see text] corresponding to spectral radius [Formula: see text] is called the principal eigenvector of [Formula: see text]. In this paper, we present some lower bounds for the spectral radius [Formula: see text] and investigate the bounds of entries of the principal eigenvector of [Formula: see text].

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A NODE-BASED MULTISCALE VULNERABILITY OF COMPLEX NETWORKS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409023068 ◽

2009 ◽

Vol 19 (02) ◽

pp. 703-710 ◽

Cited By ~ 8

Author(s):

R. CRIADO ◽

J. PELLO ◽

M. ROMANCE ◽

M. VELA-PÉREZ

Keyword(s):

Complex Networks ◽

Linear Relationship ◽

Complex Network ◽

Lower Bounds ◽

Upper And Lower Bounds ◽

Mathematical Framework

A novel node-based approach to quantify the vulnerability of a complex network is presented. The proposed measure represents a multiscale evaluation of vulnerability closely related to the edge multiscale vulnerability. In fact, a linear relationship between the edge multiscale vulnerability and the node multiscale vulnerability is stated for p = 1. Upper and lower bounds are established for other values of p. This mathematical framework is subsequently used to obtain some interesting results about the Madrid underground network.

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