Related papers: A Characterization of Level-k Realizability for Cl…
The C-Planarity problem asks for a drawing of a $\textit{clustered graph}$, i.e., a graph whose vertices belong to properly nested clusters, in which each cluster is represented by a simple closed region with no edge-edge crossings, no…
Hypergraphs are generalizations of simple graphs that allow for the representation of complex group interactions beyond pairwise relationships. Clustering coefficients quantify local link density in networks and have been widely studied for…
Phylogenetic networks provide a way to describe and visualize evolutionary histories that have undergone so-called reticulate evolutionary events such as recombination, hybridization or horizontal gene transfer. The level k of a network…
Triadic closure, the formation of a connection between two nodes in a network sharing a common neighbor, is considered a fundamental mechanism determining the clustered nature of many real-world topologies. In this work we define a static…
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…
The stochastic block model is a canonical random graph model for clustering and community detection on network-structured data. Decades of extensive study on the problem have established many profound results, among which the phase…
Community detection in networks is a key exploratory tool with applications in a diverse set of areas, ranging from finding communities in social and biological networks to identifying link farms in the World Wide Web. The problem of…
We initiate the study of coresets for clustering in graph metrics, i.e., the shortest-path metric of edge-weighted graphs. Such clustering problems are essential to data analysis and used for example in road networks and data visualization.…
Upon a matrix representation of a binary bipartite network, via the permutation invariance, a coupling geometry is computed to approximate the minimum energy macrostate of a network's system. Such a macrostate is supposed to constitute the…
Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…
Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. Clustering, community structure and assortative mixing by degree are perhaps among most prominent…
Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…
In a graph $G$, a subset of vertices $S \subseteq V(G)$ is said to be cyclable if there is a cycle containing the vertices in some order. $G$ is said to be $k$-cyclable if any subset of $k \geq 2$ vertices is cyclable. If any $k$…
In the Categorical Clustering problem, we are given a set of vectors (matrix) A={a_1,\ldots,a_n} over \Sigma^m, where \Sigma is a finite alphabet, and integers k and B. The task is to partition A into k clusters such that the median…
Hierarchical Agglomerative Clustering (HAC) is an extensively studied and widely used method for hierarchical clustering in $\mathbb{R}^k$ based on repeatedly merging the closest pair of clusters according to an input linkage function $d$.…
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…
Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…
We uncover the global organization of clustering in real complex networks. As it happens with other fundamental properties of networks such as the degree distribution, we find that real networks are neither completely random nor ordered…
Real growing networks like the WWW or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the…
$\kC$ clustering is a fundamental classification problem, where the task is to categorize the given collection of entities into $k$ clusters and come up with a representative for each cluster, so that the maximum distance between an entity…