Related papers: A Threshold For Clusters in Real-World Random Netw…
Clustering, assortativity, and communities are key features of complex networks. We probe dependencies between these attributes and find that ensembles with strong clustering display both high assortativity by degree and prominent community…
This paper presents a clustering approach that allows for rigorous statistical error control similar to a statistical test. We develop estimators for both the unknown number of clusters and the clusters themselves. The estimators depend on…
It is common in the study of networks to investigate meso-scale features to try to gain an understanding of network structure and function. For example, numerous algorithms have been developed to try to identify "communities," which are…
We study a random system of $cn$ linear equations over $n$ variables in GF(2), where each equation contains exactly $r$ variables; this is equivalent to $r$-XORSAT. \cite{ikkm,amxor} determined the clustering threshold, $c^*_r$: if…
We consider the problem of estimating the measure of subsets in very large networks. A prime tool for this purpose is the Markov Chain Monte Carlo (MCMC) algorithm. This algorithm, while extremely useful in many cases, still often suffers…
Apart from the role the clustering coefficient plays in the definition of the small-world phenomena, it also has great relevance for practical problems involving networked dynamical systems. To study the impact of the clustering coefficient…
Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance…
Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process…
We study the Axelrod's cultural adaptation model using the concept of cluster size entropy, $S_{c}$ that gives information on the variability of the cultural cluster size present in the system. Using networks of different topologies, from…
We introduce and define three types of small worlds: small worlds based on the diameter of the network (SWD), those based on the average geodesic distance between nodes (SWA), and those based on the median geodesic distance (SWMd). These…
The stochastic block model is a classical cluster-exhibiting random graph model that has been widely studied in statistics, physics and computer science. In its simplest form, the model is a random graph with two equal-sized clusters, with…
An unsupervised classification method for point events occurring on a network of lines is proposed. The idea relies on the distributional flexibility and practicality of random partition models to discover the clustering structure featuring…
A model of correlated random networks is examined, i.e. networks with correlations between the degrees of neighboring nodes. These nodes do not necessarily have to be direct neighbors, the maximum range of the correlations can be…
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…
One basic requirement of many studies is the necessity of classifying data. Clustering is a proposed method for summarizing networks. Clustering methods can be divided into two categories named model-based approaches and algorithmic…
This paper establishes asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model for clustered data when both of the number of independent…
Peer-grouping is used in many sectors for organisational learning, policy implementation, and benchmarking. Clustering provides a statistical, data-driven method for constructing meaningful peer groups, but peer groups must be compatible…
Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral…
The silhouette coefficient quantifies, for each observation, the balance between within-cluster cohesion and between-cluster separation, taking values in the range [-1,1]. The average silhouette width (ASW) is a widely used internal measure…
The correct identification of clusters is crucial for an accurate monitoring of the spread of a disease and also in many other natural, social and physical phenomena which exhibit an epidemic structure. Nevertheless, even when an accurate…