Related papers: Edge-Colored Clustering in Hypergraphs: Beyond Min…
Consider the following two ways to colour the vertices of a graph where the requirement that adjacent vertices get distinct colours is relaxed. A colouring has "defect" $d$ if each monochromatic component has maximum degree at most $d$. A…
We consider the maximum chromatic number of hypergraphs consisting of cliques that have pairwise small intersections. Designs of the appropriate parameters produce optimal constructions, but these are known to exist only when the number of…
Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods,…
Finding densely connected subsets of vertices in an unsupervised setting, called clustering or community detection, is one of the fundamental problems in network science. The edge clustering approach instead detects communities by…
Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Min $s-t$ Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization. Here, we are given a graph with edges labeled $+$…
In this paper, we use the concept of colored edge graphs to model homogeneous faults in networks. We then use this model to study the minimum connectivity (and design) requirements of networks for being robust against homogeneous faults…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
We study colored coverage and clustering problems. Here, we are given a colored point set where the points are covered by (unknown) $k$ clusters, which are monochromatic (i.e., all the points covered by the same cluster, have the same…
In this study, we address the complex issue of graph clustering in signed graphs, which are characterized by positive and negative weighted edges representing attraction and repulsion among nodes, respectively. The primary objective is to…
This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know…
How do vertices exert influence in graph data? We develop a framework for edge clustering, a new method for exploratory data analysis that reveals how both vertices and edges collaboratively accomplish directed influence in graphs,…
A hypergraph is a useful combinatorial object to model ternary or higher-order relations among entities. Clustering hypergraphs is a fundamental task in network analysis. In this study, we develop two clustering algorithms based on…
Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges…
We study clustering on graphs with multiple edge types. Our main motivation is that similarities between objects can be measured in many different metrics. For instance similarity between two papers can be based on common authors, where…
Edge-coloring problems with forbidden patterns are decision problems asking to find an edge-coloring of the input graph which avoids a homomorphism from a fixed forbidden family of edge-colored graphs. In the precolored version of these…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
We propose a new approach for defining and searching clusters in graphs that represent real technological or transaction networks. In contrast to the standard way of finding dense parts of a graph, we concentrate on the structure of edges…
In this paper we consider clustering problems in which each point is endowed with a color. The goal is to cluster the points to minimize the classical clustering cost but with the additional constraint that no color is over-represented in…
We study conditions under which an edge-coloured hypergraph has a particular substructure that contains more than the trivially guaranteed number of monochromatic edges. Our main result solves this problem for perfect matchings under…
Graph clustering is a challenging pattern recognition problem whose goal is to identify vertex partitions with high intra-group connectivity. This paper investigates a bi-objective problem that maximizes the number of intra-cluster edges of…