相关论文: Bipartite Communities

Bipartite graphs are a fundamental concept in graph theory with diverse applications. A graph is bipartite iff it contains no odd cycles, a characteristic that has many implications in diverse fields ranging from matching problems to the…

A very important problem in combinatorial optimization is partitioning a network into communities of densely connected nodes; where the connectivity between nodes inside a particular community is large compared to the connectivity between…

We investigate combinatorial properties of certain configurations of a graph partition which are related to the minimality of a cut. We show that such configurations are related to the third eigenvector of the Laplacian matrix. It is well…

Community search on bipartite graphs, especially influential community detection, has received significant attention. Existing studies use minimum vertex weights, inadequately reflecting true community influence when some vertices have low…

We study the spectrum of the normalized Laplace operator of a connected graph $\Gamma$. As is well known, the smallest nontrivial eigenvalue measures how difficult it is to decompose $\Gamma$ into two large pieces, whereas the largest…

Community detection is expensive, and the cost generally depends at least linearly on the number of vertices in the graph. We propose working with a reduced graph that has many fewer nodes but nonetheless captures key community structure.…

Community search over bipartite graphs has attracted significant interest recently. In many applications such as user-item bipartite graph in E-commerce, customer-movie bipartite graph in movie rating website, nodes tend to have attributes,…

We present and discuss a mathematical procedure for identification of small "communities" or segments within large bipartite networks. The procedure is based on spectral analysis of the matrix encoding network structure. The principal tool…

Despite being a source of rich information, graphs are limited to pairwise interactions. However, several real-world networks such as social networks, neuronal networks, etc., involve interactions between more than two nodes. Simplicial…

The hypergraph community detection problem seeks to identify groups of related nodes in hypergraph data. We propose an information-theoretic hypergraph community detection algorithm which compresses the observed data in terms of community…

Several problems such as network intrusion, community detection, and disease outbreak can be described by observations attributed to nodes or edges of a graph. In these applications presence of intrusion, community or disease outbreak is…

Community detection, also known as graph partitioning, is a well-known NP-hard combinatorial optimization problem with applications in diverse fields such as complex network theory, transportation, and smart power grids. The problem's…

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…

We study the vertex classification problem on a graph whose vertices are in $k\ (k\geq 2)$ different communities, edges are only allowed between distinct communities, and the number of vertices in different communities are not necessarily…

For a given complex square matrix $A$ with constant row sum, we establish two new eigenvalue inclusion sets. Using these bounds, first we derive bounds for the second largest and smallest eigenvalues of adjacency matrices of $k$-regular…

Spectral techniques have proved amongst the most effective approaches to graph clustering. However, in general they require explicit computation of the main eigenvectors of a suitable matrix (usually the Laplacian matrix of the graph).…

The spectrum of a network or graph $G=(V,E)$ with adjacency matrix $A$, consists of the eigenvalues of the normalized Laplacian $L= I - D^{-1/2} A D^{-1/2}$. This set of eigenvalues encapsulates many aspects of the structure of the graph,…

For a connected graph $\mathcal{G}=(V,E)$ with $n$ nodes, $m$ edges, and Laplacian matrix $\boldsymbol{{\mathit{L}}}$, a grounded Laplacian matrix $\boldsymbol{{\mathit{L}}}(S)$ of $\mathcal{G}$ is a $(n-k) \times (n-k)$ principal submatrix…

The second largest eigenvalue of a graph is an important algebraic parameter which is related with the expansion, connectivity and randomness properties of a graph. Expanders are highly connected sparse graphs. In coding theory, Expander…

A $z$-matching on a bipartite graph is a set of edges, among which each vertex of two types of the graph is adjacent to at most $1$ and at most $z$ ($\geqslant 1$) edges, respectively. The $z$-matching problem concerns finding $z$-matchings…