Related papers: Stochastic fluctuations and the detectability limi…
The EM-algorithm is a general procedure to get maximum likelihood estimates if part of the observations on the variables of a network are missing. In this paper a stochastic version of the algorithm is adapted to probabilistic neural…
In network science, assortativity refers to the tendency of links to exist between nodes with similar attributes. In social networks, for example, links tend to exist between individuals of similar age, nationality, location, race, income,…
The modularity of a graph is a parameter that measures its community structure; the higher its value (between $0$ and $1$), the more clustered the graph is. In this paper we show that the modularity of a random $3$-regular graph is at least…
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.…
The stochastic block model is a natural model for studying community detection in random networks. Its clustering properties have been extensively studied in the statistics, physics and computer science literature. Recently this area has…
An efficient and relatively fast algorithm for the detection of communities in complex networks is introduced. The method exploits spectral properties of the graph Laplacian-matrix combined with hierarchical-clustering techniques, and…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
In this paper, we study the information-theoretic limits of community detection in the symmetric two-community stochastic block model, with intra-community and inter-community edge probabilities $\frac{a}{n}$ and $\frac{b}{n}$ respectively.…
We prove the existence of an asymptotic phase transition threshold on community detectability for the spectral modularity method [M. E. J. Newman, Phys. Rev. E 74, 036104 (2006) and Proc. National Academy of Sciences. 103, 8577 (2006)]…
One of the most widely studied problem in mining and analysis of complex networks is the detection of community structures. The problem has been extensively studied by researchers due to its high utility and numerous applications in various…
We provide a proof of a recently conjectured universal bound on current fluctuations in Markovian processes. This bound establishes a link between the fluctuations of an individual observable current, the cycle affinities driving the system…
Smooth linear statistics of random permutation matrices, sampled under a general Ewens distribution, exhibit an interesting non-universality phenomenon. Though they have bounded variance, their fluctuations are asymptotically non-Gaussian…
Traditionally, community detection in graphs can be solved using spectral methods or posterior inference under probabilistic graphical models. Focusing on random graph families such as the stochastic block model, recent research has unified…
Community detection is considered as a fundamental task in analyzing social networks. Even though many techniques have been proposed for community detection, most of them are based exclusively on the connectivity structures. However, there…
Several differential equation models have been proposed to explain the formation of patterns characteristic of the grid cell network. Understanding the robustness of these patterns with respect to noise is one of the key open questions in…
The stochastic block model is one of the most studied network models for community detection. It is well-known that most algorithms proposed for fitting the stochastic block model likelihood function cannot scale to large-scale networks.…
We study the problem of community recovery and detection in multi-layer stochastic block models, focusing on the critical network density threshold for consistent community structure inference. Using a prototypical two-block model, we…
Communities of vertices within a giant network such as the World-Wide Web are likely to be vastly smaller than the network itself. However, Fortunato and Barth\'{e}lemy have proved that modularity maximization algorithms for community…
This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several…
The growing popularity of online social networks has provided researchers with access to large amount of social network data. This, coupled with the ever increasing computation speed, storage capacity and data mining capabilities, led to…