Related papers: Voltage Graphs and Cluster Consensus with Point Gr…
A cluster graph is a graph whose every connected component is a complete graph. Given a simple undirected graph $G$, a subset of vertices inducing a cluster graph is called an independent union of cliques (IUC), and the IUC polytope…
Document clustering is an unsupervised approach in which a large collection of documents (corpus) is subdivided into smaller, meaningful, identifiable, and verifiable sub-groups (clusters). Meaningful representation of documents and…
This paper presents a multiscale graph construction method using both graph and signal features. Multiscale graph is a hierarchical representation of the graph, where a node at each level indicates a cluster in a finer resolution. To obtain…
With a view on graph clustering, we present a definition of vertex-to-vertex distance which is based on shared connectivity. We argue that vertices sharing more connections are closer to each other than vertices sharing fewer connections.…
Let $\Delta$ be an oriented valued graph equipped with a group of admissible automorphisms satisfying a certain stability condition. We prove that the (coefficient-free) cluster algebra $\mathcal A(\Delta/G)$ associated to the valued…
We study the phenomenon of cluster synchrony that occurs in ensembles of coupled phase oscillators when higher-order modes dominate the coupling between oscillators. For the first time, we develop a complete analytic description of the…
This paper establishes a theoretical framework to describe the transition from consensus to stable clustering in multi-agent systems with nonlinear, cooperative interactions. We first establish a sharp threshold for consensus. For a broad…
We propose a novel model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix that models the…
A graph with a semiregular group of automorphisms can be thought of as the derived cover arising from a voltage graph. Since its inception, the theory of voltage graphs and their derived covers has been a powerful tool used in the study of…
Cluster synchronization is a phenomenon in which a network self-organizes into a pattern of synchronized sets. It has been shown that diverse patterns of stable cluster synchronization can be captured by symmetries of the network. Here we…
In this paper, we address two forms of consensus for multi-agent systems with undirected, signed, weighted, and connected communication graphs, under the assumption that the agents can be partitioned into three clusters, representing the…
Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition…
This paper proposes the matrix-weighted consensus algorithm, which is a generalization of the consensus algorithm in the literature. Given a networked dynamical system where the interconnections between agents are weighted by nonnegative…
We study the popular distributed consensus method over networks composed of a number of densely connected clusters with a sparse connection between them. In these cluster networks, the method often constitutes two-time-scale dynamics, where…
How can we find meaningful clusters in a graph robustly against noise edges? Graph clustering (i.e., dividing nodes into groups of similar ones) is a fundamental problem in graph analysis with applications in various fields. Recent studies…
For any system $\{i\}$ of particles with the trajectories $x_{i}(t)$ in $R^{d}$ on a finite time interval $[0,\tau]$ we define the interaction graph $G$. Vertices of $G$ are the particles, there is an edge between two particles $i,j$ iff…
In this paper, we present a detailed analysis of the global clustering coefficient in scale-free graphs. Many observed real-world networks of diverse nature have a power-law degree distribution. Moreover, the observed degree distribution…
In this paper we examine robust clustering behaviour with multiple nontrivial clusters for identically and globally coupled phase oscillators. These systems are such that the dynamics is completely determined by the number of oscillators N…
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of…
This article deals with the consensus problem involving agents with time-varying singularities in the dynamics or communication in undirected graph networks. Existing results provide control laws which guarantee asymptotic consensus. These…