Multilayer networks have drawn much attention in the community of network science recently. Tremendous effort has been invested to understand their structure and functions, among which centrality is one of the most effective approaches. While various metrics of centrality have been proposed for single-layer networks, a general framework of studying centrality in multiplayer networks is lacking....

Let G(V,E1) and G (V,E2) be two networks on the same vertex set V and consider the union of edges G(V,E1 ∪ E2). This paper studies the stability of the Degree, Betweenness and Eigenvector Centrality of the resultant network, G(V,E1 ∪ E2). Specifically assume v max and v max are the highest centrality vertices of G(V,E1) and G(V,E1 ∪ E2) respectively, we want to find Pr(v max = v max). ar X iv :...

A max-plus matrixA is called weakly stable if the sequence (orbit) x,A⊗x, A2⊗x, . . . does not reach an eigenvector of A for any x unless x is an eigenvector. This is in contrast to previously studied strongly stable (robust) matrices for which the orbit reaches an eigenvector with any nontrivial starting vector. Max-plus matrices are used to describe multiprocessor interactive systems for whic...

The origin of the luminosity dependence of the equivalent width (EW) of broad emission lines in AGN (the Baldwin effect) is not firmly established yet. We explore this question for the broad C iv λ1549 line using the Boroson & Green sample of the 87 z ≤ 0.5 Bright Quasar Survey (BQS) quasars. Useful UV spectra of the C iv region are available for 81 of the objects, which are used to explore 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 spreading influence in a network. However, the node spreading influence is a result of the interplay between the network topology structure and spreading dyn...

This paper studies the evolution of self appraisal, social power and interpersonal influencesfor a group of individuals who discuss and form opinions about a sequence of issues. Our empirical modelcombines the averaging rule by DeGroot to describe opinion formation processes and the reflected appraisalmechanism by Friedkin to describe the dynamics of individuals’ self appraisal and ...

Functional magnetic resonance data acquired in a task-absent condition ("resting state") require new data analysis techniques that do not depend on an activation model. In this work, we introduce an alternative assumption- and parameter-free method based on a particular form of node centrality called eigenvector centrality. Eigenvector centrality attributes a value to each voxel in the brain su...

In this paper, we analyze the second eigenvector technique of spectral partitioning on the planted partition random graph model, by constructing a recursive algorithm using the second eigenvectors in order to learn the planted partitions. The correctness of our algorithm is not based on the ratio-cut interpretation of the second eigenvector, but exploits instead the stability of the eigenvector...