Related papers: Stability of graph communities across time scales

In signed networks, some existing community detection methods treat negative connections as intercommunity links and positive ones as intracommunity links. However, it is important to recognize that negative links on real-world networks…

Despite the central role of self-assembled groups in animal and human societies, statistical tools to explain their composition are limited. We introduce a statistical framework for cross-sectional observations of groups with exclusive…

The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…

Graph embedding methods are becoming increasingly popular in the machine learning community, where they are widely used for tasks such as node classification and link prediction. Embedding graphs in geometric spaces should aid the…

A hierarchical clustering method is stable if small perturbations on the data set produce small perturbations in the result. These perturbations are measured using the Gromov-Hausdorff metric. We study the problem of stability on…

The detection of communities is an important tool used to analyze the social graph of mobile phone users. Within each community, customers are susceptible of attracting new ones, retaining old ones and/or accepting new products or services…

Many methods have been proposed to detect communities, not only in plain, but also in attributed, directed or even dynamic complex networks. In its simplest form, a community structure takes the form of a partition of the node set. From the…

Temporal Networks, and more specifically, Markovian Temporal Networks, present a unique challenge regarding the community discovery task. The inherent dynamism of these systems requires an intricate understanding of memory effects and…

In this paper, we study a notion of local stationarity for discrete time Markov chains which is useful for applications in statistics. In the spirit of some locally stationary processes introduced in the literature, we consider triangular…

Study of the cluster- or community structure of complex networks makes an important contribution to the understanding of networks at a functional level. Despite the many efforts, no definition of community has been agreed on and important…

Real complex systems are inherently time-varying. Thanks to new communication systems and novel technologies, it is today possible to produce and analyze social and biological networks with detailed information on the time of occurrence and…

Hypergraphs naturally represent higher-order interactions, which persistently appear from social interactions to neural networks and other natural systems. Although their importance is well recognized, a theoretical framework to describe…

Inferring graph structure from observations on the nodes is an important and popular network science task. Departing from the more common inference of a single graph and motivated by social and biological networks, we study the problem of…

Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping…

We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…

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…

The problem of community detection in networks is usually formulated as finding a single partition of the network into some "correct" number of communities. We argue that it is more interpretable and in some regimes more accurate to…

Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical…

Link streams model interactions over time in a wide range of fields. Under this model, the challenge is to mine efficiently both temporal and topological structures. Community detection and change point detection are one of the most…

One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…