Related papers: A note on a generalization of eigenvector centrali…
The study of hypergraphs has received a lot of attention over the past few years, however up until recently there has been no interest in systems where higher order interactions are not undirected. In this article we introduce the notion of…
A vertex $v \in V(G)$ is called $\lambda$-main if it belongs to a star set $X \subset V(G)$ of the eigenvalue $\lambda$ of a graph $G$ and this eigenvalue is main for the graph obtained from $G$ by deleting all the vertices in $X \setminus…
A hypergraph is a useful combinatorial object to model ternary or higher-order relations among entities. Clustering hypergraphs is a fundamental task in network analysis. In this study, we develop two clustering algorithms based on…
The significance of the PageRank algorithm in shaping the modern Internet cannot be overstated, and its Complex Network theory foundations continue to be a subject of research. In this article we carry out a systematic study of the…
Measures of node centrality that describe the importance of a node within a network are crucial for understanding the behavior of social networks and graphs. In this paper, we address the problems of distributed estimation and control of…
As the calculation of centrality in complex networks becomes increasingly vital across technological, biological, and social systems, precise and scalable ranking methods are essential for understanding these networks. This paper introduces…
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…
In this paper, we initiate the study of the inverse eigenvalue problem for probe graphs. A probe graph is a graph whose vertices are partitioned into probe vertices and non-probe vertices such that the non-probe vertices form an independent…
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…
We study a simple embedding technique based on a matrix of personalized PageRank vectors seeded on a random set of nodes. We show that the embedding produced by the element-wise logarithm of this matrix (1) are related to the spectral…
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…
We characterize all graphs for which there are eigenvectors of the graph Laplacian having all their components in {-1,+1} or {-1,0,+ 1}. Graphs having eigenvectors with components in {-1,+1} are called bivalent and are shown to be the…
The $\lambda$-core vertices of a graph correspond to the non-zero entries of some eigenvector of $\lambda$ for a universal adjacency matrix $\mathbf{U}$ of the graph. We define a partition of the vertex set $V$ based on the $\lambda$-core…
The standard notion of the Laplacian of a graph is generalized to the setting of a graph with the extra structure of a ``transmission`` system. A transmission system is a mathematical representation of a means of transmitting…
The computational demands of community detection algorithms such as Louvain and spectral optimization can be prohibitive for large networks. Eigenvector centrality and Katz centrality are two network statistics commonly used to describe the…
The PageRank algorithm enables to rank the nodes of a network through a specific eigenvector of the Google matrix, using a damping parameter $\alpha \in ]0,1[$. Using extensive numerical simulations of large web networks, with a special…
The calculation of centrality measures is common practice in the study of networks, as they attempt to quantify the importance of individual vertices, edges, or other components. Different centralities attempt to measure importance in…
A lot of natural language processing problems need to encode the text sequence as a fix-length vector, which usually involves aggregation process of combining the representations of all the words, such as pooling or self-attention. However,…
Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to…
We consider a broad class of walk-based, parameterized node centrality measures for network analysis. These measures are expressed in terms of functions of the adjacency matrix and generalize various well-known centrality indices, including…