Finding communities in evolving networks is a difficult task and raises issues different from the classic static detection case. We introduce an approach based on the recent vertex-centred paradigm. The proposed algorithm, named DynLOCNeSs, detects communities by scanning and evaluating each vertex neighbourhood, which can be done independently in a parallel way. It is done by means of a preference measure, using these preferences to handle community changes. We also introduce a new vertex neighbourhood preference measure, CWCN, more efficient than current existing ones in the considered context. Experimental results show the relevance of this measure and the ability of the proposed approach to detect classical community evolution patterns such as grow-shrink and merge-split.
@cite_4: 
@cite_1: In this paper we present an original approach for community detection in complex networks. The approach belongs to the family of seed-centric algorithms. However, instead of expanding communities around selected seeds as most of existing approaches do, we explore here applying an ensemble clustering approach to different network partitions derived from ego-centered communities computed for each selected seed. Ego-centered communities are themselves computed applying a recently proposed ensemble ranking based approach that allow to efficiently combine various local modularities used to guide a greedy optimization process. Results of first experiments on real world networks for which a ground truth decomposition into communities are known, argue for the validity of our approach.
@cite_3: Much of the data of scientific interest, particularly when independence of data is not assumed, can be represented in the form of information networks where data nodes are joined together to form edges corresponding to some kind of associations or relationships. Such information networks abound, like protein interactions in biology, web page hyperlink connections in information retrieval on the Web, cellphone call graphs in telecommunication, co-authorships in bibliometrics, crime event connections in criminology, etc. All these networks, also known as social networks, share a common property, the formation of connected groups of information nodes, called community structures. These groups are densely connected nodes with sparse connections outside the group. Finding these communities is an important task for the discovery of underlying structures in social networks, and has recently attracted much attention in data mining research. In this paper, we present Top Leaders, a new community mining approach that, simply put, regards a community as a set of followers congregating around a potential leader. Our algorithm starts by identifying promising leaders in a given network then iteratively assembles followers to their closest leaders to form communities, and subsequently finds new leaders in each group around which to gather followers again until convergence. Our intuitions are based on proven observations in social networks and the results are very promising. Experimental results on benchmark networks verify the feasibility and eectiveness of our new community mining approach.
@cite_27: Analyzing massive social networks challenges both high-performance computers and human understanding. These massive networks cannot be visualized easily, and their scale makes applying complex analysis methods computationally expensive. We present a region-growing method for finding a smaller, more tractable subgraph, a community, given a few example seed vertices. Unlike existing work, we focus on a small number of seed vertices, from two to a few dozen. We also present the first comparison between five algorithms for expanding a small seed set into a community. Our comparison applies these algorithms to an R-MAT generated graph component with 240 thousand vertices and 32 million edges and evaluates the community size, modularity, Kullback-Leibler divergence, conductance, and clustering coefficient. We find that our new algorithm with a local modularity maximizing heuristic based on Clauset, Newman, and Moore performs very well when the output is limited to 100 or 1 000 vertices. When run without a vertex size limit, a heuristic from McCloskey and Bader generates communities containing around 60 of the graph’s vertices and having a small conductance and modularity appropriate to the result size. A personalized PageRank algorithm based on Andersen, Lang, and Chung also performs well with respect to our metrics.
@cite_2: In local community detection by seed expansion a single cluster concentrated around few given query nodes in a graph is discovered in a localized way. Conductance is a popular objective function used in many algorithms for local community detection. Algorithms that directly optimize conductance usually add or remove one node at a time to find a local optimum. This amounts to fix a specific neighborhood structure over clusters. A natural way to avoid the problem of choosing a specific neighborhood structure is to use a continuous relaxation of conductance. This paper studies such a continuous relaxation of conductance. We show that in this setting continuous optimization leads to hard clusters. We investigate the relation of conductance with weighted kernel k-means for a single cluster, which leads to the introduction of a weighted kernel 1-mean objective function, called -conductance, where is a parameter which influences the size of the community. Conductance is obtained by setting to 0. Two algorithms for local optimization of -conductance based on the expectation maximization and the projected gradient descend method are developed, called EMc and PGDc, respectively. We show that for =0 EMc corresponds to gradient descend with an infinite step size at each iteration. We design a procedure to automatically select a value for . Performance guarantee for these algorithms is proven for a class of dense communities centered around the seeds and well separated from the rest of the network. On this class we also prove that our algorithms stay localized. A comparative experimental analysis on networks with ground-truth communities is performed using state-of-the-art algorithms based on the graph diffusion method. Our experiments indicate that EMc and PGDc stay localized and produce communities most similar to the ground.
@cite_17: Leader-driven community detection algorithms (LdCD hereafter) constitute a new trend in devising algorithms for community detection in large-scale complex networks. The basic idea is to identify some particular nodes in the target network, called leader nodes, around which local communities can be computed. Being based on local computations, they are particularly attractive to handle large-scale networks. In this paper, we describe a framework for implementing LdCD algorithms, called LICOD. We propose also a new way for evaluating performances of community detection algorithms. This consists on transforming data clustering problems into a community detection problems. External criteria for evaluating obtained clusters can then be used for comparing performances of different community detection approaches. Results we obtain show that our approach outperforms top state of the art algorithms for community detection in complex networks.
Finally, vertex-centred approaches have gained popularity as a promising new community detection method family. They rely on the principle that some vertices in the network are leaders" or seeds" and the rest are followers @cite_27 . Communities are formed by gathering followers around leaders, like in the approach @cite_3 . Although this method is more related to @math -means clustering (re-allocating the leaders) than to a true leader-follower design, the introduced idea of expanding communities around leaders considering the potential of a follower vertex (resp. a group of follower vertices) to join a leader vertex has been exploited by numerous algorithms. @cite_1 greedily expands communities around seeds and gather communities using ensemble clustering. @cite_17 starts with a careful selection of leaders before computing ranked community membership for each follower, then adjusting preferences and memberships using strategies borrowed from social choice theories until stabilisation. and @cite_2 locally expand around seed via EM or Projected Gradient Descent algorithm, using conductance to delimit communities. @cite_4 consider each vertex as a potential leader and build preference dependencies allowing to form communities. True leaders are the core of the dependencies were the rest can be considered as followers.