Related papers: Stability of graph communities across time scales
Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to temporal graphs, whose edge-sets change over discrete…
Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…
With invaluable theoretical and practical benefits, the problem of partitioning networks for community structures has attracted significant research attention in scientific and engineering disciplines. In literature, Newman's modularity…
In this work, we present a general method to establish properties of multi-dimensional continuous-time Markov chains representing stochastic reaction networks. This method consists of grouping states together (via a partition of the state…
Temporal communities result from a consistent partitioning of nodes across multiple snapshots of an evolving complex network that can help uncover how dense clusters in a network emerge, combine, split and decay with time. Current methods…
This note studies monotone Markov chains, a subclass of Markov chains with extensive applications in operations research and economics. While the properties that ensure the global stability of these chains are well studied, their…
As the complexity and size of software projects increases in real-world environments, maintaining and creating maintainable and dependable code becomes harder and more costly. Refactoring is considered as a method for enhancing the internal…
The community structure of a complex network can be determined by finding the partitioning of its nodes that maximizes modularity. Many of the proposed algorithms for doing this work by recursively bisecting the network. We show that this…
This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel…
Community detection remains an important problem in data mining, owing to the lack of scalable algorithms that exploit all aspects of available data - namely the directionality of flow of information and the dynamics thereof. Most existing…
Many empirical networks have community structure, in which nodes are densely interconnected within each community (i.e., a group of nodes) and sparsely across different communities. Like other local and meso-scale structure of networks,…
Community detection plays a key role in understanding graph structure. However, several recent studies showed that community detection is vulnerable to adversarial structural perturbation. In particular, via adding or removing a small…
Due to the advent of the expressions of data other than tabular formats, the topological compositions which make samples interrelated came into prominence. Analogically, those networks can be interpreted as social connections, dataflow…
Many algorithms to detect communities in networks typically work without any information on the cluster structure to be found, as one has no a priori knowledge of it, in general. Not surprisingly, knowing some features of the unknown…
The characterization of network community structure has profound implications in several scientific areas. Therefore, testing the algorithms developed to establish the optimal division of a network into communities is a fundamental problem…
Similar to community detection, partitioning the nodes of a network according to their structural roles aims to identify fundamental building blocks of a network. The found partitions can be used, e.g., to simplify descriptions of the…
We study a new connection between a technical measure called $\mu$-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters…
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…
The goal of community detection algorithms is to identify densely-connected units within large networks. An implicit assumption is that all the constituent nodes belong equally to their associated community. However, some nodes are more…