Related papers: A convenient trick to compute cluster sizes in a N…
The problem of finding clusters in complex networks has been extensively studied by mathematicians, computer scientists and, more recently, by physicists. Many of the existing algorithms partition a network into clear clusters, without…
Clustering algorithms frequently require the number of clusters to be chosen in advance, but it is usually not clear how to do this. To tackle this challenge when clustering within sequential data, we present a method for estimating the…
We construct a method by which we can calculate the precision with which an algorithm identifies the shape of a cluster. We present our results for several well known clustering algorithms and suggest ways to improve performance for newer…
The clustering coefficient is a valuable tool for understanding the structure of complex networks. It is widely used to analyze social networks, biological networks, and other complex systems. While there is generally a single common…
Algorithms for community detection are usually stochastic, leading to different partitions for different choices of random seeds. Consensus clustering has proven to be an effective technique to derive more stable and accurate partitions…
Suppose that $T$ is a stochastic matrix. We propose an algorithm for identifying clusters in the Markov chain associated with $T$. The algorithm is recursive in nature, and in order to identify clusters, it uses the sign pattern of a left…
We use a cluster ensemble to determine the number of clusters, k, in a group of data. A consensus similarity matrix is formed from the ensemble using multiple algorithms and several values for k. A random walk is induced on the graph…
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…
Finding a good clustering of vertices in a network, where vertices in the same cluster are more tightly connected than those in different clusters, is a useful, important, and well-studied task. Many clustering algorithms scale well,…
This paper considers cluster detection in Block Markov Chains (BMCs). These Markov chains are characterized by a block structure in their transition matrix. More precisely, the $n$ possible states are divided into a finite number of $K$…
We explore a simple mathematical model of network computation, based on Markov chains. Similar models apply to a broad range of computational phenomena, arising in networks of computers, as well as in genetic, and neural nets, in social…
Community detection, which focuses on clustering nodes or detecting communities in (mostly) a single network, is a problem of considerable practical interest and has received a great deal of attention in the research community. While being…
A popular way to cluster a temporal network is to transform it into a sequence of networks, also called slices, where each slice corresponds to a time interval and contains the vertices and edges existing in that interval. A reason to…
A novel framework for consensus clustering is presented which has the ability to determine both the number of clusters and a final solution using multiple algorithms. A consensus similarity matrix is formed from an ensemble using multiple…
The random networks enriched with additional structures as metric and group-symmetry in background metric space are investigated. The important quantities like he clustering coefficient as well as the mean degree of separation in such…
We obtain the clustering coefficient, the degree-dependent local clustering, and the mean clustering of networks with arbitrary correlations between the degrees of the nearest-neighbor vertices. The resulting formulas allow one to determine…
Many real-world networks display a natural bipartite structure. It is necessary and important to study the bipartite networks by using the bipartite structure of the data. Here we propose a modification of the clustering coefficient given…
The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…
We develop an algorithm to detect community structure in complex networks. The algorithm is based on spectral methods and takes into account weights and links orientations. Since the method detects efficiently clustered nodes in large…
Clustering mechanisms are essential in certain multiuser networks for achieving efficient resource utilization. This lecture note presents the theory of coalition formation as a useful tool for distributed clustering problems. We reveal the…