Related papers: Solution for the properties of a clustered network

Tensor clustering has become an important topic, specifically in spatio-temporal modeling, due to its ability to cluster spatial modes (e.g., stations or road segments) and temporal modes (e.g., time of the day or day of the week). Our…

A network is said to have the properties of a small world if a suitably defined average distance between any two nodes is proportional to the logarithm of the number of nodes, $N$. In this paper, we present a novel derivation of the…

The topological patterns exhibited by many real-world networks motivate the development of topology-based methods for assessing the similarity of networks. However, extracting topological structure is difficult, especially for large and…

A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…

We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. This imperfect communication poses a fundamental…

While there has been much interest in adapting conventional clustering procedures---and in higher dimensions, persistent homology methods---to directed networks, little is known about the convergence of such methods. In order to even…

We propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient. Among other things, our results indicate that increased clustering leads to a decrease in the size of the…

Unraveling the emergence of collective learning in systems of coupled artificial neural networks points to broader implications for machine learning, neuroscience, and society. Here we introduce a minimal model that condenses several recent…

In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…

Network data appears in very diverse applications, like biological, social, or sensor networks. Clustering of network nodes into categories or communities has thus become a very common task in machine learning and data mining. Network data…

Our general subject is the emergence of phases, and phase transitions, in large networks subjected to a few variable constraints. Our main result is the analysis, in the model using edge and triangle subdensities for constraints, of a sharp…

A microscopic theory of linear response based on the Vlasov equation is extended to systems having spheroidal equilibrium shape. The solution of the linearized Vlasov equation, which gives a semiclassical version of the random phase…

We obtain the clustering coefficient, the degree-dependent local clustering, and the mean clustering of networks with arbitrary correlations between the degrees of the nearest-neighbor vertices. The resulting formulas allow one to determine…

We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses…

Tensor networks, which have been traditionally used to simulate many-body physics, have recently gained significant attention in the field of machine learning due to their powerful representation capabilities. In this work, we propose a…

In this work we explain how to properly use mean-field methods to solve the inverse Ising problem when the phase space is clustered, that is many states are present. The clustering of the phase space can occur for many reasons, e.g. when a…

Clustering is a fundamental task in data analysis, and spectral clustering has been recognized as a promising approach to it. Given a graph describing the relationship between data, spectral clustering explores the underlying cluster…

We propose a multi-phase approach to explore network structures. In this method, structure analysis is not carried out on the observed network directly. Instead, certain similarity measures of the nodes are derived from the network firstly,…

The problem of network-constrained averaging is to compute the average of a set of values distributed throughout a graph G using an algorithm that can pass messages only along graph edges. We study this problem in the noisy setting, in…

Statistical methods for reconstructing networks from repeated measurements typically assume that all measurements are generated from the same underlying network structure. This need not be the case, however. People's social networks might…