Related papers: Random Walks, Markov Processes and the Multiscale …
Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a…
We address the problem of community detection in networks by introducing a general definition of Markov stability, based on the difference between the probability fluxes of a Markov chain on the network at different time scales. The…
The complexity of biological, social and engineering networks makes it desirable to find natural partitions into communities that can act as simplified descriptions and provide insight into the structure and function of the overall system.…
Many real systems can be represented as networks whose analysis can be very informative regarding the original system's organisation. In the past decade community detection received a lot of attention and is now an active field of research.…
From traffic flows on road networks to electrical signals in brain networks, many real-world networks contain modular structures of different sizes and densities. In the networks where modular structures emerge due to coupling between nodes…
Recent years have seen a surge of interest in the analysis of complex networks, facilitated by the availability of relational data and the increasingly powerful computational resources that can be employed for their analysis. Naturally, the…
We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize 'perturbation modularity', defined as the autocovariance of…
Multiscale community detection can be viewed from a dynamical perspective within the Markov Stability framework, which uses the diffusion of a Markov process on the graph to uncover intrinsic network substructures across all scales. Here we…
The analysis of stability of community structure is an important problem for scientists from many fields. Here, we propose a new framework to reveal hidden properties of community structure by quantitatively analyzing the dynamics of Potts…
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…
Potts model is a powerful tool to uncover community structure in complex networks. Here, we propose a new framework to reveal the optimal number of communities and stability of network structure by quantitatively analyzing the dynamics of…
Many systems exhibit complex temporal dynamics due to the presence of different processes taking place simultaneously. An important task in such systems is to extract a simplified view of their time-dependent network of interactions.…
Community structure is a critical feature of real networks, providing insights into nodes' internal organization. Nowadays, with the availability of highly detailed temporal networks such as link streams, studying community structures…
Modularity maximization has been one of the most widely used approaches in the last decade for discovering community structure in networks of practical interest in biology, computing, social science, statistical mechanics, and more.…
Communities are clusters of nodes with a higher than average density of internal connections. Their detection is of great relevance to better understand the structure and hierarchies present in a network. Modularity has become a standard…
In network science, a group of nodes connected with each other at higher probability than with those outside the group is referred to as a community. From the perspective that individual communities are associated with functional modules…
The detection of community structure in networks is intimately related to finding a concise description of the network in terms of its modules. This notion has been recently exploited by the Map equation formalism (M. Rosvall and C.T.…
Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the…
We focus on the detection of communities in multi-scale networks, namely networks made of different levels of organization and in which modules exist at different scales. It is first shown that methods based on modularity are not…
We propose a generative model to detect globally optimal community structures in networks by utilizing random walks. Sophisticated parameter optimization algorithms are developed based on the Markov chain Monte Carlo methods to overcome…