Related papers: Cluster synchronization on hypergraphs
In this paper, the investigation is first motivated by showing two examples of simple regular symmetrical graphs, which have the same structural parameters, such as average distance, degree distribution and node betweenness centrality, but…
Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal…
Synchronization of identical harmonic oscillators interconnected via position, velocity, and acceleration couplings is studied. How to construct a complex Laplacian matrix representing the overall coupling is presented. It is shown that the…
We present an extended analysis, based on the dynamics towards synchronization of a system of coupled oscillators, of the hierarchy of communities in complex networks. In the synchronization process, different structures corresponding to…
We present a structural clustering algorithm for large-scale datasets of small labeled graphs, utilizing a frequent subgraph sampling strategy. A set of representatives provides an intuitive description of each cluster, supports the…
Classifying whole images is a classic problem in machine learning, and graph neural networks are a powerful methodology to learn highly irregular geometries. It is often the case that certain parts of a point cloud are more important than…
Most existing semi-supervised graph-based clustering methods exploit the supervisory information by either refining the affinity matrix or directly constraining the low-dimensional representations of data points. The affinity matrix…
Network synchronization is an emerging phenomenon in complex networks. The spectrum of Laplacian matrix will be immensely helpful for getting the network dynamics information. Especially, network synchronizability is characterized by the…
We analyze the synchronization dynamics of phase oscillators far from the synchronization manifold, including the onset of synchronization on scale-free networks with low and high clustering coefficients. We use normal coordinates and…
Recent developments in complex systems have witnessed that many real-world scenarios, successfully represented as networks are not always restricted to binary interactions but often include higher-order interactions among the nodes. These…
We study the problem of clustering nodes in a dynamic graph, where the connections between nodes and nodes' cluster memberships may change over time, e.g., due to community migration. We first propose a dynamic stochastic block model that…
Local clustering aims to identify specific substructures within a large graph without any additional structural information of the graph. These substructures are typically small compared to the overall graph, enabling the problem to be…
Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of…
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…
Correlation clustering provides a method for separating the vertices of a signed graph into the optimum number of clusters without specifying that number in advance. The main goal in this type of clustering is to minimize the number of…
Hypergraphs are a useful abstraction for modeling multiway relationships in data, and hypergraph clustering is the task of detecting groups of closely related nodes in such data. Graph clustering has been studied extensively, and there are…
The acknowledged model for networks of collaborations is the hypergraph model. Nonetheless when it comes to be visualized hypergraphs are transformed into simple graphs. Very often, the transformation is made by clique expansion of the…
Statistical analysis and node clustering in hypergraphs constitute an emerging topic suffering from a lack of standardization. In contrast to the case of graphs, the concept of nodes' community in hypergraphs is not unique and encompasses…
Semi-supervised Laplacian regularization, a standard graph-based approach for learning from both labelled and unlabelled data, was recently demonstrated to have an insignificant high dimensional learning efficiency with respect to…
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…