Related papers: Identifying symmetries and predicting cluster sync…
Cluster algebras have recently become an important player in mathematics and physics. In this work, we investigate them through the lens of modern data science, specifically with techniques from network science and machine learning. Network…
Synchrony patterns characterize network states in which nodes organize into clusters based on their synchronized dynamics. The synchronized clusters may further exhibit either active or inactive states. The simultaneous invariance of active…
Graph clustering is an unsupervised machine learning method that partitions the nodes in a graph into different groups. Despite achieving significant progress in exploiting both attributed and structured data information, graph clustering…
Symmetries found through automorphisms or graph fibrations provide important insights in network analysis. Symmetries identify clusters of robust synchronization in the network which improves the understanding of the functionality of…
We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the…
Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the $n{\times}n$ graph Laplacian matrix to extract its $k$ leading…
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…
We build upon recent advances in graph signal processing to propose a faster spectral clustering algorithm. Indeed, classical spectral clustering is based on the computation of the first k eigenvectors of the similarity matrix' Laplacian,…
By a small-size complex network of coupled chaotic Hindmarsh-Rose circuits, we study experimentally the stability of network synchronization to the removal of shortcut links. It is shown that the removal of a single shortcut link may…
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…
Synchrony patterns describe network states in which nodes of a coupled dynamical system are grouped into clusters based on synchronization between nodes. Beyond simple synchrony, synchronized clusters may also exhibit active or inactive…
Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the…
We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity…
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
The topological information of a network can be retrieved equivalently from its complement consisting of the same nodes but complementary edges. Hence the partition of a network into certain substructures based on given criteria should be…
Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…
The behaviour and functioning of a variety of complex physical and biological systems depend on the spatial organisation of their constituent units, and on the presence and formation of clusters of functionally similar or related…
A natural approach to analyze interaction data of form "what-connects-to-what-when" is to create a time-series (or rather a sequence) of graphs through temporal discretization (bandwidth selection) and spatial discretization (vertex…
Finding groups of connected individuals in large graphs with tens of thousands or more nodes has received considerable attention in academic research. In this paper, we analyze three main issues with respect to the recent influx of papers…
Graph clustering is the problem of identifying sparsely connected dense subgraphs (clusters) in a given graph. Proposed clustering algorithms usually optimize various fitness functions that measure the quality of a cluster within the graph.…