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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
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.
Fixed Points of Graph Peeling
, 2013
"... Degree peeling is used to study complex networks. It corresponds to a decomposition of the graph into vertex groups of increasing minimum degree. However, the peeling value of a vertex is nonlocal in this context since it relies on the connections the vertex has to groups above it. We explore a di ..."
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Degree peeling is used to study complex networks. It corresponds to a decomposition of the graph into vertex groups of increasing minimum degree. However, the peeling value of a vertex is nonlocal in this context since it relies on the connections the vertex has to groups above it. We explore a different way to decompose a network into edge layers such that the local peeling value of the vertices on each layer does not depend on their nonlocal connections with the other layers. This corresponds to the decomposition of a graph into subgraphs that are invariant with respect to degree peeling, i.e. they are fixed points. We introduce in this context a method to partition the edges of a graph into fixed points of degree peeling, called the iterativeedgecore decomposition. Information from this decomposition is used to formulate a notion of vertex diversity based on Shannon’s entropy. We illustrate the usefulness of this decomposition in social network analysis. Our method can be used for community detection and graph visualization.