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Truss Decomposition in Massive Networks
"... The ktruss is a type of cohesive subgraphs proposed recently for the study of networks. While the problem of computing most cohesive subgraphs is NPhard, there exists a polynomial time algorithm for computing ktruss. Compared with kcore which is also efficient to compute, ktruss represents the ..."
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The ktruss is a type of cohesive subgraphs proposed recently for the study of networks. While the problem of computing most cohesive subgraphs is NPhard, there exists a polynomial time algorithm for computing ktruss. Compared with kcore which is also efficient to compute, ktruss represents the “core ” of a kcore that keeps the key information of, while filtering out less important information from, the kcore. However, existing algorithms for computing ktruss are inefficient for handling today’s massive networks. We first improve the existing inmemory algorithm for computing ktruss in networks of moderate size. Then, we propose two I/Oefficient algorithms to handle massive networks that cannot fit in main memory. Our experiments on real datasets verify the efficiency of our algorithms and the value of ktruss. 1.
Mobility Performance of
 MacrocellAssisted Small Cells in Manhattan Model,” Vehicular Technology Conference (VTC Spring), 2014 IEEE 79th
, 2014
"... Recent research efforts have made notable progress in improving the performance of (exhaustive) maximal clique enumeration (MCE). However, existing algorithms still suffer from exploring the huge search space of MCE. Furthermore, their results are often undesirable as many of the returned maximal c ..."
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Recent research efforts have made notable progress in improving the performance of (exhaustive) maximal clique enumeration (MCE). However, existing algorithms still suffer from exploring the huge search space of MCE. Furthermore, their results are often undesirable as many of the returned maximal cliques have large overlapping parts. This redundancy leads to problems in both computational efficiency and usefulness of MCE. In this paper, we aim at providing a concise and complete summary of the set of maximal cliques, which is useful to many applications. We propose the notion of τvisible MCE to achieve this goal and design algorithms to realize the notion. Based on the refined output space, we further consider applications including an efficient computation of the topk results with diversity and an interactive clique exploration process. Our experimental results demonstrate that our approach is capable of producing output of high usability and our algorithms achieve superior efficiency over classic MCE algorithms.
Streaming Algorithms for kcore Decomposition
"... A kcore of a graph is a maximal connected subgraph in which every vertex is connected to at least k vertices in the subgraph. kcore decomposition is often used in largescale network analysis, such as community detection, protein function prediction, visualization, and solving NPHard problems on ..."
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A kcore of a graph is a maximal connected subgraph in which every vertex is connected to at least k vertices in the subgraph. kcore decomposition is often used in largescale network analysis, such as community detection, protein function prediction, visualization, and solving NPHard problems on real networks efficiently, like maximal clique finding. In many realworld applications, networks change over time. As a result, it is essential to develop efficient incremental algorithms for streaming graph data. In this paper, we propose the first incremental kcore decomposition algorithms for streaming graph data. These algorithms locate a small subgraph that is guaranteed to contain the list of vertices whose maximum kcore values have to be updated, and efficiently process this subgraph to update the kcore decomposition. Our results show a significant reduction in runtime compared to nonincremental alternatives. We show the efficiency of our algorithms on different types of real and synthetic graphs, at different scales. For a graph of 16 million vertices, we observe speedups reaching a million times, relative to the nonincremental algorithms. 1.
Fast algorithms for maximal clique enumeration with limited memory
 In Proceedings of the ACM SIGKDD international
, 2012
"... Maximal clique enumeration (MCE) is a longstanding problem in graph theory and has numerous important applications. Though extensively studied, most existing algorithms become impractical when the input graph is too large and is diskresident. We first propose an efficient partitionbased algorith ..."
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Maximal clique enumeration (MCE) is a longstanding problem in graph theory and has numerous important applications. Though extensively studied, most existing algorithms become impractical when the input graph is too large and is diskresident. We first propose an efficient partitionbased algorithm for MCE that addresses the problem of processing large graphs with limited memory. We then further reduce the high cost of CPU computation of MCE by a careful nested partition based on a cost model. Finally, we parallelize our algorithm to further reduce the overall running time. We verified the efficiency of our algorithms by experiments in large realworld graphs.
Efficient core maintenance in large dynamic graphs
 CoRR
"... Abstract—The kcore decomposition in a graph is a fundamental problem for social network analysis. The problem of kcore decomposition is to calculate the core number for every node in a graph. Previous studies mainly focus on kcore decomposition in a static graph. There exists a linear time algori ..."
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Abstract—The kcore decomposition in a graph is a fundamental problem for social network analysis. The problem of kcore decomposition is to calculate the core number for every node in a graph. Previous studies mainly focus on kcore decomposition in a static graph. There exists a linear time algorithm for kcore decomposition in a static graph. However, in many realworld applications such as online social networks and the Internet, the graph typically evolves over time. In such applications, a key issue is to maintain the core numbers of nodes when the graph changes over time. A simple implementation is to perform the linear time algorithm to recompute the core number for every node after the graph is updated. Such simple implementation is expensive when the graph is very large. In this paper, we propose a new efficient algorithm to maintain the core number for every node in a dynamic graph. Our main result is that only certain nodes need to update their core numbers when the graph is changed by inserting/deleting an edge. We devise an efficient algorithm to identify and recompute the core numbers of such nodes. The complexity of our algorithm is independent of the graph size. In addition, to further accelerate the algorithm, we develop two pruning strategies by exploiting the lower and upper bounds of the core number. Finally, we conduct extensive experiments over both realworld and synthetic datasets, and the results demonstrate the efficiency of the proposed algorithm. Index Terms—Core maintenance, kcore decomposition, dynamic graphs 1
Distributed kCore Decomposition
"... Abstract—Several novel metrics have been proposed in recent literature in order to study the relative importance of nodes in complex networks. Among those, kcoreness has found a number of applications in areas as diverse as sociology, proteinomics, graph visualization, and distributed system analys ..."
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Abstract—Several novel metrics have been proposed in recent literature in order to study the relative importance of nodes in complex networks. Among those, kcoreness has found a number of applications in areas as diverse as sociology, proteinomics, graph visualization, and distributed system analysis and design. This paper proposes new distributed algorithms for the computation of the kcoreness of a network, a process also known as k–core decomposition. This technique (i) allows the decomposition, over a set of connected machines, of very large graphs, when size does not allow storing and processing them on a single host, and (ii) enables the runtime computation of kcores in “live ” distributed systems. Lower bounds on the algorithms complexity are given, and an exhaustive experimental analysis on realworld datasets is provided. a sample graph, consider Figure 1. Note that by definition cores are nested, meaning that nodes belonging to the 3core belong to the2core and1core, as well. Larger values of “coreness”, though, clearly correspond to nodes with a more central position in the network structure. Index Terms—kcore decomposition, Graph analysis, Bulk Synchronous Parallel 1
Large Scale Cohesive Subgraphs Discovery for Social Network Visual Analysis
"... Graphs are widely used in large scale social network analysis nowadays. Not only analysts need to focus on cohesive subgraphs to study patterns among social actors, but also normal users are interested in discovering what happening in their neighborhood. However, effectively storing large scale soci ..."
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Graphs are widely used in large scale social network analysis nowadays. Not only analysts need to focus on cohesive subgraphs to study patterns among social actors, but also normal users are interested in discovering what happening in their neighborhood. However, effectively storing large scale social network and efficiently identifying cohesive subgraphs is challenging. In this work we introduce a novel subgraph concept to capture the cohesion in social interactions, and propose an I/O efficient approach to discover cohesive subgraphs. Besides, we propose an analytic system which allows users to perform intuitive, visual browsing on large scale social networks. Our system stores the network as a social graph in the graph database, retrieves a local cohesive subgraph based on the input keywords, and then hierarchically visualizes the subgraph out on orbital layout, in which more important social actors are located in the center. By summarizing textual interactions between social actors as tag cloud, we provide a way to quickly locate active social communities and their interactions in a unified view. 1.
Multiresolution Social Network Community Identification and Maintenance on Big Data Platform
"... Abstract—Community identification in social networks is of great interest and with dynamic changes to its graph representation and content, the incremental maintenance of community poses significant challenges in computation. Moreover, the intensity of community engagement can be distinguished at mu ..."
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Abstract—Community identification in social networks is of great interest and with dynamic changes to its graph representation and content, the incremental maintenance of community poses significant challenges in computation. Moreover, the intensity of community engagement can be distinguished at multiple levels, resulting in a multiresolution community representation that has to be maintained over time. In this paper, we first formalize this problem using the kcore metric projected at multiple k values, so that multiple community resolutions are represented with multiple kcore graphs. We then present distributed algorithms to construct and maintain a multikcore graph, implemented on the scalable bigdata platform Apache HBase. Our experimental evaluation results demonstrate orders of magnitude speedup by maintaining multikcore incrementally over complete reconstruction. Our algorithms thus enable practitioners to create and maintain communities at multiple resolutions on different topics in rich social network content simultaneously. Keywordscommunity identification; Big Data analytics; kcore; dynamic social networks; distributed computing I.
Locally Estimating Core Numbers
"... Abstract—Graphs are a powerful way to model interactions and relationships in data from a wide variety of application domains. In this setting, entities represented by vertices at the “center ” of the graph are often more important than those associated with vertices on the “fringes”. For example, c ..."
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Abstract—Graphs are a powerful way to model interactions and relationships in data from a wide variety of application domains. In this setting, entities represented by vertices at the “center ” of the graph are often more important than those associated with vertices on the “fringes”. For example, central nodes tend to be more critical in the spread of information or disease and play an important role in clustering/community formation. Identifying such “core ” vertices has recently received additional attention in the context of network experiments, which analyze the response when a random subset of vertices are exposed to a treatment (e.g. inoculation, free product samples, etc). Specifically, the likelihood of having many central vertices in any exposure subset can have a significant impact on the experiment. We focus on using kcores and core numbers to measure the extent to which a vertex is central in a graph. Existing algorithms for computing the core number of a vertex require the entire graph as input, an unrealistic scenario in many real world applications. Moreover, in the context of network experiments, the subgraph induced by the treated vertices is only known in a probabilistic sense. We introduce a new method for estimating the core number based only on the properties of the graph within a region of radius δ around the vertex, and prove an asymptotic error bound of our estimator on random graphs. Further, we empirically validate the accuracy of our estimator for small values of δ on a representative corpus of real data sets. Finally, we evaluate the impact of improved local estimation on an open problem in network experimentation posed by Ugander et al. I.
Rectangle counting in large bipartite graphs (long version),” http://www.cse.cuhk. edu.hk/∼jcheng/rect.pdf
, 2013
"... Abstract—Rectangles are the smallest cycles (i.e., cycles of length 4) and most elementary substructures in a bipartite graph. Similar to triangle counting in unipartite graphs, rectangle counting has many important applications where data is modeled as bipartite graphs. However, efficient algorit ..."
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Abstract—Rectangles are the smallest cycles (i.e., cycles of length 4) and most elementary substructures in a bipartite graph. Similar to triangle counting in unipartite graphs, rectangle counting has many important applications where data is modeled as bipartite graphs. However, efficient algorithms for rectangle counting are lacking. We propose three different types of algorithms to cope with different data volumes and the availability of computing resources. We verified the efficiency of our algorithms with experiments on both large realworld and synthetic bipartite graphs. Keywordsbipartite graphs; rectangle counting; I.