Related papers: Laplacian Eigenvector Centrality
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…
In network data analysis, it is becoming common to work with a collection of graphs that exhibit \emph{heterogeneity}. For example, neuroimaging data from patient cohorts are increasingly available. A critical analytical task is to identify…
This article deals with the spectra of Laplacians of weighted graphs. In this context, two objects are of fundamental importance for the dynamics of complex networks: the second eigenvalue of such a spectrum (called algebraic connectivity)…
Measures of complex network analysis, such as vertex centrality, have the potential to unveil existing network patterns and behaviors. They contribute to the understanding of networks and their components by analyzing their structural…
Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as…
For a given infinite connected graph $G=(V,E)$ and an arbitrary but fixed conductance function $c$, we study an associated graph Laplacian $\Delta_{c}$; it is a generalized difference operator where the differences are measured across the…
Network centrality is a foundational concept for quantifying the importance of nodes within a network. Many traditional centrality measures--such as degree and betweenness centrality--are purely structural and often overlook the dynamics…
Metric networks are network-shaped, one-dimensional structures on which one can solve differential equations to simulate a wide range of physical systems including conjugated molecules, photonic crystals, quantum mechanics in waveguide…
In this paper, we present a framework for studying the following fundamental question in network analysis: How should one assess the centralities of nodes in an information/influence propagation process over a social network? Our framework…
We study the popular centrality measure known as effective conductance or in some circles as information centrality. This is an important notion of centrality for undirected networks, with many applications, e.g., for random walks,…
The analysis of complex networks has so far revolved mainly around the role of nodes and communities of nodes. However, the dynamics of interconnected systems is commonly focalised on edge processes, and a dual edge-centric perspective can…
The original contributions of this paper are twofold: a new understanding of the influence of noise on the eigenvectors of the graph Laplacian of a set of image patches, and an algorithm to estimate a denoised set of patches from a noisy…
We extend the concept of eigenvector centrality to multiplex networks, and introduce several alternative parameters that quantify the importance of nodes in a multi-layered networked system, including the definition of vectorial-type…
Graphs (i.e., networks) have become an integral tool for the representation and analysis of relational data. Advances in data gathering have lead to multi-relational data sets which exhibit greater depth and scope. In certain cases, this…
Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs.…
Eigenvector-based centrality measures are among the most popular centrality measures in network science. The underlying idea is intuitive and the mathematical description is extremely simple in the framework of standard, mono-layer…
Lattice structures play a central role in spectral graph theory, offering analytical insight into diffusion, synchronization, and transport processes on regular discrete spaces. While their spectral properties are completely characterized…
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 our previously published algorithm, we analyze the eigenvectors of the generalized Laplacian for two metric graphs occurring in practical applications. As expected, localization of an eigenvector is rare and the network should be…
Almost equitable partitions (AEPs) have been linked to cluster synchronization in oscillatory systems, highlighting the importance of structure in collective network dynamics. We provide a general spectral framework that formalizes this…