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Although many successful ensemble clustering approaches have been developed in recent years, there are still two limitations to most of the existing approaches. First, they mostly overlook the issue of uncertain links, which may mislead the…

Machine Learning · Statistics 2016-06-06 Dong Huang , Jian-Huang Lai , Chang-Dong Wang

We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning…

Social and Information Networks · Computer Science 2023-09-15 Alexander Belyi , Stanislav Sobolevsky , Alexander Kurbatski , Carlo Ratti

This paper proposes a new algorithm for solving maximal cliques for simple undirected graphs using the theory of prime numbers. A novel approach using prime numbers is used to find cliques and ends with a discussion of the algorithm.

Data Structures and Algorithms · Computer Science 2007-05-23 Dhananjay D. Kulkarni , Shekhar Verma , Prashant

Given a set A in Z/NZ we may form a Cayley sum graph G_A on vertex set Z/NZ by joining i to j if and only if i + j is in A. We investigate the extent to which performing this construction with a random set A simulates the generation of a…

Combinatorics · Mathematics 2007-05-23 Ben Green

In this paper we consider the clustering coefficient and clustering function in a random graph model proposed by Krioukov et al.~in 2010. In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are…

Probability · Mathematics 2020-12-18 Nikolaos Fountoulakis , Pim van der Hoorn , Tobias Müller , Markus Schepers

In this paper, we relatively extend the definition of global clustering coefficient to another clustering, which we call it relative clustering coefficient. The idea of this definition is to ignore the edges in the network that the…

Computational Geometry · Computer Science 2021-06-10 Elena Farahbakhsh Touli , Oscar Lindberg

Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic tractability: if the clique-width of a graph class ${\cal G}$ is bounded by a constant, a wide range of problems that are NP-complete in general…

Combinatorics · Mathematics 2021-12-23 Konrad K. Dabrowski , Matthew Johnson , Daniël Paulusma

We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of…

Probability · Mathematics 2019-08-24 Mindaugas Bloznelis , Jerzy Jaworski , Valentas Kurauskas

An uncertain graph $\mathcal{G} = (V, E, p : E \rightarrow (0,1])$ can be viewed as a probability space whose outcomes (referred to as \emph{possible worlds}) are subgraphs of $\mathcal{G}$ where any edge $e\in E$ occurs with probability…

Data Structures and Algorithms · Computer Science 2017-10-17 Matteo Ceccarello , Carlo Fantozzi , Andrea Pietracaprina , Geppino Pucci , Fabio Vandin

The global clustering coefficient is an effective measure for analyzing and comparing the structures of complex networks. The random annulus graph is a modified version of the well-known Erd\H{o}s-R\'{e}nyi random graph. It has been…

Methodology · Statistics 2025-10-20 Mingao Yuan

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…

Physics and Society · Physics 2022-07-19 Robert E. Kooij , Nikolaj Horsevad Sørensen , Roland Bouffanais

This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper…

Data Structures and Algorithms · Computer Science 2024-06-06 Steinar Laenen , He Sun

We introduce a clustering coefficient for nondirected and directed hypergraphs, which we call the quad clustering coefficient. We determine the average quad clustering coefficient and its distribution in real-world hypergraphs and compare…

Physics and Society · Physics 2024-04-08 Gyeong-Gyun Ha , Izaak Neri , Alessia Annibale

A statistical network model with overlapping communities can be generated as a superposition of mutually independent random graphs of varying size. The model is parameterized by the number of nodes, the number of communities, and the joint…

Probability · Mathematics 2024-12-19 Tommi Gröhn , Joona Karjalainen , Lasse Leskelä

A clique colouring of a graph is a colouring of the vertices so that no maximal clique is monochromatic (ignoring isolated vertices). The smallest number of colours in such a colouring is the clique chromatic number. In this paper, we study…

Probability · Mathematics 2016-11-08 Colin McDiarmid , Dieter Mitsche , Pawel Pralat

It is shown how to construct a clique graph in which properties of cliques of a fixed order in a given graph are represented by vertices in a weighted graph. Various definitions and motivations for these weights are given. The detection of…

Physics and Society · Physics 2011-01-04 T. S. Evans

We study preferential attachment mechanisms in random graphs that are parameterized by (i) a constant bias affecting the degree-biased distribution on the vertex set and (ii) the distribution of times at which new vertices are created by…

Probability · Mathematics 2017-10-09 Benjamin Bloem-Reddy , Peter Orbanz

If $\Gamma$ is a graph for which every edge is in exactly one clique of order $\omega$, then one can form a new graph with vertex set equal to these cliques. This is a generalization of the line graph of $\Gamma$. We discover many general…

Combinatorics · Mathematics 2025-02-26 Robert R. Petro , Connor M. Phillips

Counts of small subgraphs, or graphlet counts, are widely applicable to measure graph similarity. Computing graphlet counts can be computationally expensive and may pose obstacles in network analysis. We study the role of cliques in…

Social and Information Networks · Computer Science 2024-01-09 Anthony Bonato , Zhiyuan Zhang

Attributed graph clustering is challenging as it requires joint modelling of graph structures and node attributes. Recent progress on graph convolutional networks has proved that graph convolution is effective in combining structural and…

Machine Learning · Computer Science 2019-06-05 Xiaotong Zhang , Han Liu , Qimai Li , Xiao-Ming Wu