Related papers: Stability of graph communities across time scales

This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…

Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to…

Community detection algorithms attempt to find the best clusters of nodes in an arbitrary complex network. Multi-scale ("multiresolution") community detection extends the problem to identify the best network scale(s) for these clusters. The…

Model selection is a major challenge in non-parametric clustering. There is no universally admitted way to evaluate clustering results for the obvious reason that no ground truth is available. The difficulty to find a universal evaluation…

Complex networks play a crucial role in understanding physical, biological, social and technological systems. One of the most relevant features of graphs representing real systems is community structure. In this paper, for a specific…

Upper bounds are derived on the total variation distance between the invariant distributions of two stochastic matrices differing on a subset W of rows. Such bounds depend on three parameters: the mixing time and the minimal expected…

We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…

There has been substantial interest in estimating the value of a graph parameter, i.e., of a real-valued function defined on the set of finite graphs, by querying a randomly sampled substructure whose size is independent of the size of the…

We propose a general form of community detecting functions for finding the communities or the optimal partition of a random network, and examine the concentration and stability of the function values using the bounded difference martingale…

Inferring cluster structure in microarray datasets is a fundamental task for the -omic sciences. A fundamental question in Statistics, Data Analysis and Classification, is the prediction of the number of clusters in a dataset, usually…

Structural balance theory predicts that triads in networks gravitate towards stable configurations. The theory has been verified for undirected graphs. Since real-world networks are often directed, we introduce a novel method for…

Many natural Markov chains fail to mix to their stationary distribution in polynomially many steps. Often, this slow mixing is inevitable since it is computationally intractable to sample from their stationary measure. Nevertheless, Markov…

The discovery of community structure is a common challenge in the analysis of network data. Many methods have been proposed for finding community structure, but few have been proposed for determining whether the structure found is…

We have found that known community identification algorithms produce inconsistent communities when the node ordering changes at input. We propose two metrics to quantify the level of consistency across multiple runs of an algorithm:…

There are many scales at which to quantify stability in spatial and ecological networks. Local-scale analyses focus on specific nodes of the spatial network, while regional-scale analyses consider the whole network. Similarly, species- and…

Community structure is an important structural property that extensively exists in various complex networks. In the past decade, much attention has been paid to the design of community-detection methods, but analyzing the behaviors of the…

Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides…

Many algorithms have been proposed in the last ten years for the discovery of dynamic communities. However, these methods are seldom compared between themselves. In this article, we propose a generator of dynamic graphs with planted…

The task of \emph{community detection} in a graph formalizes the intuitive task of grouping together subsets of vertices such that vertices within clusters are connected tighter than those in disparate clusters. This paper approaches…

We consider the problem of testing graph cluster structure: given access to a graph $G=(V, E)$, can we quickly determine whether the graph can be partitioned into a few clusters with good inner conductance, or is far from any such graph?…