On the relationship between Gaussian stochastic blockmodels and label propagation algorithms

The problem of community detection receives great attention in recent years. Many methods have been proposed to discover communities in networks. In this paper, we propose a Gaussian stochastic blockmodel that uses Gaussian distributions to fit weight of edges in networks for non-overlapping community detection. The maximum likelihood estimation of this model has the same objective function as general label propagation with node preference. The node preference of a specific vertex turns out to be a value proportional to the intra-community eigenvector centrality (the corresponding entry in principal eigenvector of the adjacency matrix of the subgraph inside that vertex's community) under maximum likelihood estimation. Additionally, the maximum likelihood estimation of a constrained version of our model is highly related to another extension of label propagation algorithm, namely, the label propagation algorithm under constraint. Experiments show that the proposed Gaussian stochastic blockmodel performs well on various benchmark networks.Comment: 22 pages, 17 figure

Local Edge Betweenness based Label Propagation for Community Detection in Complex Networks

Nowadays, identification and detection community structures in complex networks is an important factor in extracting useful information from networks. Label propagation algorithm with near linear-time complexity is one of the most popular methods for detecting community structures, yet its uncertainty and randomness is a defective factor. Merging LPA with other community detection metrics would improve its accuracy and reduce instability of LPA. Considering this point, in this paper we tried to use edge betweenness centrality to improve LPA performance. On the other hand, calculating edge betweenness centrality is expensive, so as an alternative metric, we try to use local edge betweenness and present LPA-LEB (Label Propagation Algorithm Local Edge Betweenness). Experimental results on both real-world and benchmark networks show that LPA-LEB possesses higher accuracy and stability than LPA when detecting community structures in networks.Comment: 6 page

On the Analysis of a Label Propagation Algorithm for Community Detection

This paper initiates formal analysis of a simple, distributed algorithm for community detection on networks. We analyze an algorithm that we call \textsc{Max-LPA}, both in terms of its convergence time and in terms of the "quality" of the communities detected. \textsc{Max-LPA} is an instance of a class of community detection algorithms called \textit{label propagation} algorithms. As far as we know, most analysis of label propagation algorithms thus far has been empirical in nature and in this paper we seek a theoretical understanding of label propagation algorithms. In our main result, we define a clustered version of \er random graphs with clusters $V_1, V_2,..., V_k$ where the probability $p$, of an edge connecting nodes within a cluster $V_i$ is higher than $p'$, the probability of an edge connecting nodes in distinct clusters. We show that even with fairly general restrictions on $p$ and $p'$ ($p = \Omega(\frac{1}{n^{1/4-\epsilon}})$ for any $\epsilon > 0$, $p' = O(p^2)$, where $n$ is the number of nodes), \textsc{Max-LPA} detects the clusters $V_1, V_2,..., V_n$ in just two rounds. Based on this and on empirical results, we conjecture that \textsc{Max-LPA} can correctly and quickly identify communities on clustered \er graphs even when the clusters are much sparser, i.e., with $p = \frac{c\log n}{n}$ for some $c > 1$.Comment: 17 pages. Submitted to ICDCN 201

Practical Minimum Cut Algorithms

The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our algorithm is based on cluster contraction using label propagation and Padberg and Rinaldi's contraction heuristics [SIAM Review, 1991]. We give both sequential and shared-memory parallel implementations of our algorithm. Extensive experiments on both real-world and generated instances show that our algorithm finds the optimal cut on nearly all instances significantly faster than other state-of-the-art algorithms while our error rate is lower than that of other heuristic algorithms. In addition, our parallel algorithm shows good scalability