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Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…

Clustering is a fundamental approach to understanding data patterns, wherein the intuitive Euclidean distance space is commonly adopted. However, this is not the case for implicit cluster distributions reflected by qualitative attribute…

Much recent research activity has been devoted to empirical study and theoretical models of complex networks (random graphs) with three qualitative features: power-law degree distribution, local clustering of edges, and small diameter. We…

Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…

It has been shown that many complex networks shared distinctive features, which differ in many ways from the random and the regular networks. Although these features capture important characteristics of complex networks, their applicability…

Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…

In active learning for graph-structured data, Graph Neural Networks (GNNs) have shown effectiveness. However, a common challenge in these applications is the underutilization of crucial structural information. To address this problem, we…

With inspiration from Random Forests (RF) in the context of classification, a new clustering ensemble method---Cluster Forests (CF) is proposed. Geometrically, CF randomly probes a high-dimensional data cloud to obtain "good local…

Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects…

We introduce a minimal extended evolving model for small-world networks which is controlled by a parameter. In this model the network growth is determined by the attachment of new nodes to already existing nodes that are geographically…

Graph clustering (or community detection) has long drawn enormous attention from the research on web mining and information networks. Recent literature on this topic has reached a consensus that node contents and link structures should be…

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…

Higher-order structures of networks, namely, small subgraphs of networks (also called network motifs), are widely known to be crucial and essential to the organization of networks. There has been a few work studying the community detection…

In the last years the Prisoner Dilemma (PD) has become a paradigm for the study of the emergence of cooperation in spatially structured populations. Such structure is usually assumed to be given by a graph. In general, the success of…

Graph clustering has been studied extensively on both plain graphs and attributed graphs. However, all these methods need to partition the whole graph to find cluster structures. Sometimes, based on domain knowledge, people may have…

Many complex systems in the real world can be characterized by attributed networks. To mine the potential information in these networks, deep embedded clustering, which obtains node representations and clusters simultaneously, has been paid…

Graph clustering, or community detection, is the task of identifying groups of closely related objects in a large network. In this paper we introduce a new community-detection framework called LambdaCC that is based on a specially weighted…

Motivated by widely observed examples in nature, society and software, where groups of already related nodes arrive together and attach to an existing network, we consider network growth via sequential attachment of linked node groups, or…

Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes…

Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or…