Understanding community structure in social media is critical due to its broad applications such as friend recommendations, link predictions and collaborative filtering. However, there is no widely accepted definition of community in literature. Existing work use structure related metrics such as modularity and function related metrics such as ground truth to measure the performance of community detection algorithms, while ignoring an important metric, size of the community. [1] suggests that the size of community with strong ties in social media should be limited to 150. As we discovered in this paper, the majority of the communities obtained by many popular community detection algorithms are either very small or very large. Too small communities don't have practical value and too large communities contain weak connections therefore not stable. In this paper, we compare various community detection algorithms considering the following metrics: size of the communities, coverage of the communities, extended modularity, triangle participation ratio, and user interest in the same community. We also propose a simple clique based algorithm for community detection as a baseline for the comparison. Experimental results show that both our proposed algorithm and the well-accepted disjoint algorithm InfoMap perform well in all the metrics.
There exist many community detection algorithms in literature. We can categorize them into disjoint algorithms and overlapping algorithms, based on whether the identified communities have overlap or not. Infomap @cite_10 stands out as the most popular and widely used disjoint algorithm. The Infomap algorithm is based on random walks on networks combined with coding theory with the intent of understanding how information flows within a network. Multilevel @cite_14 is a heuristic based algorithm based on modularity optimization. Multilevel first assigns every node to a separate community, then selects a node and checks the neighboring nodes attempting to group the neighboring node with the selected node into a community if the grouping results in an increase in modularity. Newman's Leading Eigenvector @cite_2 works by moving the maximization process to the eigenspectrum to maximize modularity by using a matrix known as the modularity matrix. Fast Greedy @cite_6 is based upon modularity as well. It uses a greedy approach to optimize modularity. In the category of overlapping algorithm, Clique Percolation Method @cite_9 is the most prominent which merges two cliques into a community if they overlap more than a threshold.
@cite_14 @cite_9 @cite_6 @cite_2 @cite_10
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We have recently introduced a multistep extension of the greedy algorithm for modularity optimization. The extension is based on the idea that merging l pairs of communities (l>1) at each iteration prevents premature condensation into few large communities. Here, an empirical formula is presented for the choice of the step width l that generates partitions with (close to) optimal modularity for 17 real-world and 1100 computer-generated networks. Furthermore, an in-depth analysis of the communities of two real-world networks (the metabolic network of the bacterium E. coli and the graph of coappearing words in the titles of papers coauthored by Martin Karplus) provides evidence that the partition obtained by the multistep greedy algorithm is superior to the one generated by the original greedy algorithm not only with respect to modularity, but also according to objective criteria. In other words, the multistep extension of the greedy algorithm reduces the danger of getting trapped in local optima of modularity and generates more reasonable partitions. Many networks, indifferent of their function and scope, converge to a scale-free architecture in which the degree distribution approximately follows a power law. Meanwhile, many of those scale-free networks are found to be naturally divided into communities of densely connected nodes, known as community structure. Finding this community structure is a fundamental but challenging topic in network science. Since Newman's suggestion of using modularity as a measure to qualify the strength of community structure, many efficient methods that find community structure based on maximizing modularity have been proposed. However, there is a lack of approximation algorithms that provide provable quality bounds for the problem. In this paper, we propose polynomial-time approximation algorithms for the modularity maximization problem together with their theoretical justifications in the context of scale-free networks. We prove that the solutions of the proposed algorithms, even in the worst-case, are optimal up to a constant factor for scale-free networks with either bidirectional or unidirectional links. Even though our focus in this work is not on designing another empirically good algorithms to detect community structure, experiments on real-world networks suggest that the proposed algorithm is competitive with the state-of-the-art modularity maximization algorithm. We propose using five data-driven community detection approaches from social networks to partition the label space in the task of multi-label classification as an alternative to random partitioning into equal subsets as performed by RAkELd. We evaluate modularity-maximizing using fast greedy and leading eigenvector approximations, infomap, walktrap and label propagation algorithms. For this purpose, we propose to construct a label co-occurrence graph (both weighted and unweighted versions) based on training data and perform community detection to partition the label set. Then, each partition constitutes a label space for separate multi-label classification sub-problems. As a result, we obtain an ensemble of multi-label classifiers that jointly covers the whole label space. Based on the binary relevance and label powerset classification methods, we compare community detection methods to label space divisions against random baselines on 12 benchmark datasets over five evaluation measures. We discover that data-driven approaches are more efficient and more likely to outperform RAkELd than binary relevance or label powerset is, in every evaluated measure. For all measures, apart from Hamming loss, data-driven approaches are significantly better than RAkELd ( α = 0 . 05 ), and at least one data-driven approach is more likely to outperform RAkELd than a priori methods in the case of RAkELd’s best performance. This is the largest RAkELd evaluation published to date with 250 samplings per value for 10 values of RAkELd parameter k on 12 datasets published to date. Many social networks and complex systems are found to be naturally divided into clusters of densely connected nodes, known as community structure (CS). Finding CS is one of fundamental yet challenging topics in network science. One of the most popular classes of methods for this problem is to maximize Newman's modularity. However, there is a littleunderstood on how well we can approximate the maximum modularity as well as the implications of finding community structure with provable guarantees. In this paper, we settle definitely the approximability of modularity clustering, proving that approximating the problem within any (multiplicative) positive factor is intractable, unless P = NP. Yet we propose the first additive approximation algorithm for modularity clustering with a constant factor. Moreover, we providea rigorous proof that a CS with modularity arbitrary close to maximum modularity QOPT might bear no similarity to the optimal CS of maximum modularity. Thus even when CS with near-optimal modularity are found, other verification methods are needed to confirm the significance of the structure.