Keywords: dynamic Social Network, Community detection, Centrality measures, Modularity function.

Transcription

1 Volume 6, Issue 1, January 2016 ISSN: X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: An Efficient and Fast Algorithm for Detecting Community Structure in Dynamic Social Network A. Meligy, Ahmed H. Samak, Mai E. Saad Faculty of Science, Menofia University, Egypt Abstract: Community structure is one of the most important properties in social networks. Many algorithms have been proposed to automatically detect communities in static networks but few studies have considered the detection of communities in dynamic networks. This article aims to detecting communities in dynamic social networks. In this paper, we introduce a new algorithm for updating the network communities at any time point by using the information from the previous snapshots as well as network changes whereas the static methods has to be performed on the whole network snapshot up to each time point. The static methods we are comparing to namely Louvain method, Danon algorithm, and SOM algorithm. The experimental results show that our algorithm achieves high modularity and fast running time against static algorithms. Keywords: dynamic Social Network, Community detection, Centrality measures, Modularity function. I. INTRODUCTION Social networks can be generally modeled by a graph, where is the set of vertices and it represents the social actors, and represents the set of edges connecting pairs of vertices and it represents the interactions between them. For a better analysis of a social network, it is usually decomposed into subunits or communities, i.e., a group of nodes sharing something like a group of friends in a social network or a group of web pages dealing with the same subject for instance. Communities are often defined using the network topology as groups of nodes with many links inside the groups but a few links between them. Real-world social networks, however, are not always static. Most studies focus on analyzing communities in static networks, and a few studies investigate the dynamics of communities in evolving social networks. An evolving network is often defined as a sequence of static networks, each of them representing the state of the network at different timestamps, shown in figure 1 [1]. Most complex networks of the real world networks evolve over time. Representing networks with graphs, this evolution can be modeled as the creation or removal of vertices and/or edges over time [2]. On an online social network (such as Facebook, Flicker, and Twitter) people start new relationship with each other, joining in or withdrawing from groups. Any of these changes seems to make a little effect to the structure of the network. Figure 1: Snapshot graphs Since each snapshot is a static graph, the first approach to compute communities on an evolving network is to use a community detection algorithm suited for static graphs on each snapshot. Studies on community detection on static networks can be found on an excellent surveys like [3,4].The main issue after detecting communities at each snapshot is to identify which community has evolved in to which community at time 1 these is the matching problem. A community may merge with another one, split, appear, or disappear overtime. The first approach to solve the matching problem in the context of evolving communities is [5]. It is based on the concept that two communities at successive timesteps are matched if they share a certain number of nodes and have similar size. This matching approach has been generalized in [6] where the authors define many similar rules to handle other cases of communities evolution: merge, split, appearance and disappearance. 2016, IJARCSSE All Rights Reserved Page 65

2 The other approach, which has not been widely followed, is using directly the temporal information during the community detection process. The major lake is now validation tools. However, there are quality functions for static network that people can use to evaluate their algorithms, such general quality functions or validation tools do not exist for evolving networks. In [7] the quality function is modified to integrate evolution. This paper splits the quality function in two terms: a part for the quality of the current snapshot and a part to ensure stability. In [8] Instead of modifying the quality function, Kim et al compute communities at time and if two nodes are in the same community at time and are also connected at, then the weight of the link between them is increased or decreased of a given factor to increase smooth-ness of a modularity optimization algorithm. Studies on community detection on dynamic networks can be found in an excellent survey [1]. II. PRELIMINARIES Notations Throughout this paper, we will use the notation proposed by Nguyen et al in [9]. We assume that undirected unweighted graph with nodes and edges representing a social network. The network community structure is denoted by, where is a community of. For each vertex, let are the community containing and the set of its adjacent communities, respectively. A dynamic network is a sequence of network snapshots evolving over time, with being a state of dynamic network recorded at time. Let be the change in term of the whole network with and denote the sets of vertices and edges to be added or removed from the network at time. Quality function The most popularity quality function is the modularity of Newman and Girvan [10]. The quality of a detected network community structure is often measured by a modularity function to quantify how good a partition is. Modularity can be formulated as be an where is the number of communities, is the total number of edges joining vertices of community,and is the sum of the degrees of the vertices of. In the above formula, the first term is the fraction of edges of the network inside the community, whereas the second term represents the expected fraction of edges that would be there if the network were a random network with the same degree for each vertex. The modularity of a partition is a scalar value between and. The higher modularity, the better the partition is [11]. III. METHOD DESCRIPTION Although one can run any of the static methods, to cluster snapshots of a dynamic graph from scratch, it has several disadvantage: First, the long running time on large networks. Second, optimizations of modularity suffer from local optima. Third, have same reaction approximately to small changes to some local part of the network. In this paper, we propose an algorithm for updating the network communities from previous known structure without reclustering from scratch. We process on network changes only, taking into account the previous network structure. This network changes can be one of newnode, removenode, newedge, removeedge whose details are as follows [9]: newnode ( ): A new node together with its associated edges are introduced. could come with no or more than one new edge(s). removenode ( ): A node and its adjacent edges are removed from the network. newedge( ): A new edge connecting two existing nodes is introduced. removeedge ( ): An existing edge in the network is removed. In this paper, we introduce two algorithms for updating community structure in only two cases (1) New node (2) New edge. Algorithms The first step of our method is to use any of the static community detection algorithms to obtain an initial community structure, in order to process further. 1) New node: The first case when new node and its associated edges are introduced. In this case we first put in a lone community, then compute the graph modularity when new node in a lone community. After that we compute each 2016, IJARCSSE All Rights Reserved Page 66

3 value of modularity when new node changes its initial community to each one of its adjacent communities, finally compare between them, the higher modularity, the better partition for the network. Note when new node come with no associated edges, we put in alone community, and leave the other communities as well as the overall modularity intact. The details of our algorithm are described as follows: Input: New Node with associated links; current structure. Output: An updated structure. 1: Create a new community of only ; 2: compute the graph modularity when new_node at a lone community. 3: for do 4: compute the value of modularity when change its community to the community of its neighbor. 5: end for 6: 7: 8: if 9: update 10: else 11: return Note that, we pre-processed above algorithm by pre-processing steps in [12]. These pre-processing steps will enhance the algorithm, and will make it execute with better results. 2) New edge: In the second case, a new edge connecting two existing vertices is introduced. In this case, we will use the algorithm of [9]. According to [9]this new edge can be divided into two cases : Intra-community link: totally inside a community. Inter-community link: connects two communities and. Lemma 1: For any, if then adding an edge within will increase its modularity contribution [9]. Theorem 1: if is a community of the current snapshot of, then adding any intra-community link to will not split it into smaller modules [9]. Theorem 2: Assume that a new edge is added to. Let and. If will increase the overall modularity [9]. then joining Corollary 1: if the condition in Theorem 2 is not satisfied, then neither nor its neighbors should be moved to [9]. We will do some modification to this algorithm [9] by adding pre-processing steps in [12]. These pre-processing steps capable of raising the modularity of algorithm, and make it execute with better results. IV. EXPERIMENTAL RESULTS In this section, we present the experimental results of our strategy on detecting the communities of dynamic social network. In particular, we will show in experiments the following quantities: modularity values, and the running time of our algorithms in comparison with static method when performed on the whole network snapshot up to each time point. The static methods we are comparing to 1) Louvain method (LM) [13], 2) Danon algorithm [14], 3) Self-organizing map (SOM) [15]. As our algorithm requires initial community structure, we use static algorithm we comparing to at each time to obtain basic structure. As a final comment, our algorithms identifying the network community structure at any time point by utilizing the information from the previous snapshots instead of computing from scratch up to each time point. Real networks We chose 6 networks whose features are reported in Table 1 to perform our experiments. Table 1. Real-World datasets NO. No. nodes No. edges Ref. 1 Karate [16] 2 Dolphins [17] [18] 2016, IJARCSSE All Rights Reserved Page 67 to

4 Common adjective and 4 noun adjacencies in David [19] Copperfield (adjnoun) [20] [21] Zachary's karate club: This is an undirected social network of friendship between 34 members of a karate club at US university. Edges connect individuals who were observed to interact outside the activities of the club. Dolphin social network: Contains an undirected social network of frequent associations of 62 dolphins living in New Zealand. Edges were set between animals that were seen together more often than expected by chance. Political Books: This dataset is the Amazon co-purchasing network with 105 books about US. Nodes are books and edges represent co-purchasing of books by the same buyers. Common adjective and noun adjacencies in David Copperfield: The network of common adjective and noun adjacencies for the novel "David Copperfield" by Charles Dickens. Nodes represent the most commonly occurring adjectives and nouns in the book. Edges connect words that occur in adjacent position in the text of the book. American college dataset: This dataset contains 115 nodes representing teams. An edge exists between two vertices if there is match between two teams. More games happen among teams within the same community than teams from different community. Jass musician network: This dataset is the collaboration network of jazz bands. There are 198 nodes representing the bands, and 2742 edges connecting the bands if there is at least one musician in common. Results 1) New node: The first case when we added a new random node to each of the above social networks, and compare the modularity values, and the running time when using our algorithm which we refer to as Dynamic algorithm with the modularity values when using static algorithm. The obtained results are reported on Table 2, Table 3, and Table 4. Table 2. Results of New_Node using Louvain as static algorithm Static Louvain modularity Time modularity Time Modularity Time Karate Dolphins adjnoun Table 3. Results of New_Node using Danon as static algorithm Static Danon modularity Time Modularity Time Modularity Time Karate Dolphins adjnoun Table 4. Results of New_Node using SOM as static algorithm Static SOM modularity Time modularity Time modularity Time Karate Dolphins , IJARCSSE All Rights Reserved Page 68

5 adjnoun ) New edge: In the second case we added a new edge between two vertices randomly. After that, we compare the modularity value, and the running time. The obtained results are shown in Table 5, Table 6, and Table 7. Table 5. Results of New_Edge using Louvain as static algorithm Static Louvain Modularity Time modularity Time modularity Time Karate Dolphins adjnoun Table 6. Results of New_Edge using Danon as static algorithm Static Danon Modularity Time modularity Time modularity Time Karate Dolphins adjnoun Table 7. Results of New_Edge using SOM as static algorithm Static SOM modularity Time modularity Time modularity Time Karate Dolphins adjnoun V. CONCLUSION In this paper, we introduce a new algorithm for identifying community structure in dynamic social network. Our algorithm updating the network communities at any time point by using the basic community structure and processes on the network changes only whereas static algorithm has to be performed on the whole network snapshot up to each time point. The static methods we are comparing to namely Louvain method, Danon algorithm, and SOM algorithm. Experimental results show that our algorithms achieve better result in modularity values, and fast running time against static algorithms. REFERENCES [1] T. Aynaud, J.-L. Guillaume, Q. Wang, and E. Fleury. Communities in evolving networks: definitions, detections and analysis techniques [2] M. Seifi, J.-L. Guillaume : Community Cores in Evolving Networks, Mining Social Network Dynamic 2012 Workshop (MSND), In conjunction with the international conference World Wide Web WWW 2012, Lyon, France, pp (2012) 2016, IJARCSSE All Rights Reserved Page 69

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