相关论文: Bipartite Communities

The independence complex of a graph $G=(V,E)$ is the simplicial complex $I(G)$ on vertex set $V$ whose simplices are the independent sets in $G$. We present new lower bounds on the eigenvalues of the $k$-dimensional Laplacian $L_k(I(G))$ in…

A \emph{co-bipartite chain} graph is a co-bipartite graph in which the neighborhoods of the vertices in each clique can be linearly ordered with respect to inclusion. It is known that the maximum cut problem (MaxCut) is NP-Hard in…

We apply spectral clustering and multislice modularity optimization to a Los Angeles Police Department field interview card data set. To detect communities (i.e., cohesive groups of vertices), we use both geographic and social information…

Given a bipartite graph $G(V= (A \cup B),E)$ with $n$ vertices and $m$ edges and a function $b \colon V \to \mathbb{Z}_+$, a $b$-matching is a subset of edges such that every vertex $v \in V$ is incident to at most $b(v)$ edges in the…

With the emergence of social networks, online platforms dedicated to different use cases, and sensor networks, the emergence of large-scale graph community detection has become a steady field of research with real-world applications.…

In this paper, some main eigenvalues and eigenvectors of the politics matrix are investigated. The number of upper-class families in a society is the number of eigenvalues which are very close to 1. An algorithm to identify all the…

Listing dense subgraphs in large graphs plays a key task in varieties of network analysis applications like community detection. Clique, as the densest model, has been widely investigated. However, in practice, communities rarely form as…

Several graph data mining, signal processing, and machine learning downstream tasks rely on information related to the eigenvectors of the associated adjacency or Laplacian matrix. Classical eigendecomposition methods are powerful when the…

Community detection in graphs identifies groups of nodes with denser connections within the groups than between them, and while existing studies often focus on optimizing detection performance, memory constraints become critical when…

Laplacian Eigenvectors of the graph constructed from a data set are used in many spectral manifold learning algorithms such as diffusion maps and spectral clustering. Given a graph constructed from a random sample of a $d$-dimensional…

We revisit the theoretical performances of Spectral Clustering, a classical algorithm for graph partitioning that relies on the eigenvectors of a matrix representation of the graph. Informally, we show that Spectral Clustering works well as…

The eigenvalue problem of a graph Laplacian matrix $L$ arising from a simple, connected and undirected graph has been given more attention due to its extensive applications, such as spectral clustering, community detection, complex network,…

Community detection in graphs is the problem of finding groups of vertices which are more densely connected than they are to the rest of the graph. This problem has a long history, but it is undergoing a resurgence of interest due to the…

This paper studies the problem of detecting the presence of a small dense community planted in a large Erd\H{o}s-R\'enyi random graph $\mathcal{G}(N,q)$, where the edge probability within the community exceeds $q$ by a constant factor.…

In $k$-hypergraph matching, we are given a collection of sets of size at most $k$, each with an associated weight, and we seek a maximum-weight subcollection whose sets are pairwise disjoint. More generally, in $k$-hypergraph $b$-matching,…

This work presents conjectures about eigenvalues of matrices associated with $k$-path graphs, the algebraic connectivity, defined as the second smallest eigenvalue of the Laplacian matrix, and the $\alpha$-index, as the largest eigenvalue…

We address the following question: When a randomly chosen regular bipartite multi--graph is drawn in the plane in the ``standard way'', what is the distribution of its maximum size planar matching (set of non--crossing disjoint edges) and…

Complex networks can be typically broken down into groups or modules. Discovering this "community structure" is an important step in studying the large-scale structure of networks. Many algorithms have been proposed for community detection…

Let $\mathcal{P}$ and $\mathcal{P}'$ be finite partitions of the set $V$. Finding good correspondences between the parts of $\mathcal{P}$ and those of $\mathcal{P}'$ is helpful in classification, pattern recognition, and network analysis.…

This paper establishes new upper bounds for the sum of the $k$ largest eigenvalues of symmetric matrices. When applied to the adjacency matrix of a graph, our results improve upon a related bound due to Mohar {\bf [On the sum of k largest…