Related papers: A Threshold For Clusters in Real-World Random Netw…
In this paper, we consider sparse networks consisting of a finite number of non-overlapping communities, i.e. disjoint clusters, so that there is higher density within clusters than across clusters. Both the intra- and inter-cluster edge…
An analytical approach to calculating bond percolation thresholds, sizes of $k$-cores, and sizes of giant connected components on structured random networks with non-zero clustering is presented. The networks are generated using a…
This paper studies the design of cluster experiments to estimate the global treatment effect in the presence of network spillovers. We provide a framework to choose the clustering that minimizes the worst-case mean-squared error of the…
Dynamic networks are increasingly being usedd to model real world datasets. A challenging task in their analysis is to detect and characterize clusters. It is useful for analyzing real-world data such as detecting evolving communities in…
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…
A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…
Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced…
In this paper, a random clique network model to mimic the large clustering coefficient and the modular structure that exist in many real complex networks, such as social networks, artificial networks, and protein interaction networks, is…
Researchers have long observed that the ``small-world" property, which combines the concepts of high transitivity or clustering with a low average path length, is ubiquitous for networks obtained from a variety of disciplines, including…
There are many cluster analysis methods that can produce quite different clusterings on the same dataset. Cluster validation is about the evaluation of the quality of a clustering; "relative cluster validation" is about using such criteria…
This paper considers the problem of inference in cluster randomized experiments when cluster sizes are non-ignorable. Here, by a cluster randomized experiment, we mean one in which treatment is assigned at the cluster level. By…
Detecting clusters or communities in large real-world graphs such as large social or information networks is a problem of considerable interest. In practice, one typically chooses an objective function that captures the intuition of a…
The idea underlying the modal formulation of density-based clustering is to associate groups with the regions around the modes of the probability density function underlying the data. This correspondence between clusters and dense regions…
We demonstrate that a tree-based theory for various dynamical processes yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance…
Data clustering is the process of identifying natural groupings or clusters within multidimensional data based on some similarity measure. Clustering is a fundamental process in many different disciplines. Hence, researchers from different…
We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in…
We investigate the onset of the discontinuous percolation transition in small-world hyperbolic networks by studying the systems-size scaling of the typical largest cluster approaching the transition, $p\nearrow p_{c}$. To this end, we…
Meso-scale structures are network features where nodes with similar properties are grouped together instead of being treated individually. In this work, we provide formal and mathematical definitions of three such structures: assortative…
In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…
This paper investigates the validity of Kleinberg's axioms for clustering functions with respect to the quite popular clustering algorithm called $k$-means. While Kleinberg's axioms have been discussed heavily in the past, we concentrate…