Related papers: Large Values of the Clustering Coefficient
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized…
This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…
Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its…
Subspace clustering is the problem of clustering data points into a union of low-dimensional linear/affine subspaces. It is the mathematical abstraction of many important problems in computer vision, image processing and machine learning. A…
Graph clustering aims to partition nodes into distinct clusters based on their similarity, thereby revealing relationships among nodes. Nevertheless, most existing methods do not fully utilize these edge weights. Leveraging edge weights in…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
A set $S\subseteq V$ of vertices of a graph $G$ is a $c$-clustered set if it induces a subgraph with components of order at most $c$ each, and $\alpha_c(G)$ denotes the size of a largest $c$-clustered set. For any graph $G$ on $n$ vertices…
We study the scenario of graph-based clustering algorithms such as spectral clustering. Given a set of data points, one first has to construct a graph on the data points and then apply a graph clustering algorithm to find a suitable…
Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for…
Silhouette coefficient is an established internal clustering evaluation measure that produces a score per data point, assessing the quality of its clustering assignment. To assess the quality of the clustering of the whole dataset, the…
Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition…
Many real-world networks have high clustering among vertices: vertices that share neighbors are often also directly connected to each other. A network's clustering can be a useful indicator of its connectedness and community structure.…
With the recent popularity of graphical clustering methods, there has been an increased focus on the information between samples. We show how learning cluster structure using edge features naturally and simultaneously determines the most…
The Cluster Variation Method known in statistical mechanics and condensed matter is revived for weighted bipartite networks. The decomposition of a Hamiltonian through a finite number of components, whence serving to define variable…
Subgraph counts - in particular the number of occurrences of small shapes such as triangles - characterize properties of random networks, and as a result have seen wide use as network summary statistics. However, subgraphs are typically…
The objective functions used in spectral clustering are usually composed of two terms: i) a term that minimizes the local quadratic variation of the cluster assignments on the graph and; ii) a term that balances the clustering partition and…
This paper presents a graph bundling algorithm that agglomerates edges taking into account both spatial proximity as well as user-defined criteria in order to reveal patterns that were not perceivable with previous bundling techniques. Each…
Given a weighted and complete graph G = (V, E), V denotes the set of n objects to be clustered, and the weight d(u, v) associated with an edge (u, v) belonging to E denotes the dissimilarity between objects u and v. The diameter of a…