Related papers: Clustering Phase Transitions and Hysteresis: Pitfa…
We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-\delta}$ in addition to nearest neighbour connections. This system has been shown to exhibit…
We study the influence of clustering, more specifically triangles, on cascading failures in interdependent networks or systems, in which we model the dependence between comprising systems using a dependence graph. First, we propose a new…
The emergence of clustering and coarsening in crowded ensembles of self-propelled agents is studied using a lattice model in one-dimension. The persistent exclusion process, where particles move at directions that change randomly at a low…
Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of $g$ fraction of the entire population in the smallest clusters. Here we show…
Nowadays there is a multitude of measures designed to capture different aspects of network structure. To be able to say if the structure of certain network is expected or not, one needs a reference model (null model). One frequently used…
Experimental systems with a first order phase transition will often exhibit hysteresis when out of equilibrium. If defects are present, the hysteresis loop can have different shapes: with small disorder the hysteresis loop has a macroscopic…
Biclustering is used for simultaneous clustering of the observations and variables when there is no group structure known \textit{a priori}. It is being increasingly used in bioinformatics, text analytics, etc. Previously, biclustering has…
Interest in the analysis of networks has grown rapidly in the new millennium. Consequently, we promote renewed attention to a certain methodological approach introduced in 1974. Over the succeeding decade, this…
Clustering a group of vertices in networks facilitates applications across different domains, such as social computing and Internet of Things. However, challenges arises for clustering networks with increased scale. This paper proposes a…
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…
Critical phase transitions have proven to be a powerful concept to capture the phenomenology of many systems, including deeply non-equilibrium ones like living systems. The study of these phase transitions has overwhelmingly relied on…
The internal organization of complex networks often has striking consequences on either their response to external perturbations or on their dynamical properties. In addition to small-world and scale-free properties, clustering is the most…
Clusters appear in nature in a diversity of contexts, involving distances as long as the cosmological ones, and down to atoms and molecules and the very small nuclear size. They also appear in several other scenarios, in particular in…
Predicting labels of nodes in a network, such as community memberships or demographic variables, is an important problem with applications in social and biological networks. A recently-discovered phase transition puts fundamental limits on…
We study a one parameter family of random graph models that spans a continuum between traditional random graphs of the Erd\H{o}s-R\'enyi type, where there is no underlying structure, and percolation models, where the possible edges are…
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…
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…
We study a model of network with clustering and desired node degree. The original purpose of the model was to describe optimal structures of scientific collaboration in the European Union. The model belongs to the family of exponential…
Large ensembles of globally coupled chaotic neural networks undergo a transition to complete synchronization for high coupling intensities. The onset of this fully coherent behavior is preceded by a regime where clusters of networks with…
We study Strauss's model of a network with clustering and present an analytic mean-field solution which is exact in the limit of large network size. Previous computer simulations have revealed a degenerate region in the model's parameter…