Efficient Core Maintenance in Large Dynamic Graphs

Abstract

Abstract-The k-core decomposition in a graph is a fundamental problem for social network analysis. The problem of k-core decomposition is to calculate the core number for every node in a graph. Previous studies mainly focus on k-core decomposition in a static graph. There exists a linear time algorithm for k-core decomposition in a static graph. However, in many real-world applications such as online social networks and the Internet, the graph typically evolves over time. Under such applications, a key issue is to maintain the core number of nodes given 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 number given the graph is changed by inserting/deleting an edge. We devise an efficient algorithm to identify and recompute the core number 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 real-world and synthetic datasets, and the results demonstrate the efficiency of the proposed algorithm.

Influential community search in large networks

“…In the literature, the maximal k-core is widely used to represent cohesive communities of a graph [2,22,4,16]. Instead of general cohesive communities, in this work, we seek to find influential communities in a graph.…”

“…Then, after inserting (u, v), every tree-i for i > cmin + 1 will not be updated. This is because when inserting an edge, the core numbers of the nodes increase by at most one [16]. As a result, each i-influential community for i > cmin +1 does not change, and thus every tree-i remains unchanged.…”

“…After deleing a node, the algorithm calls Algorithm 6 and Algorithm 7 to dynamically maintain the core numbers of the remaining nodes (lines 10-11). Notice that Algorithm 6 and Algorithm 7 generalize the core maintenance algorithm independently proposed in [16,20] to handle the case of node deletion 2 . Here we implement this core maintenance algorithm by dynamically updating the support of each node u (denoted by xu), which is defined as the number of neighbors whose updated core numbers are no smaller thancu.…”

Streaming algorithms for k-core decomposition

“…Concurrently with our work, Li et al [20] published a report on incremental algorithms for core decomposition. Our algorithms differ from theirs in two important aspects: (1) They propose quadratic complexity incremental algorithms, whereas our algorithms have linear complexity.…”

Multi-resolution Social Network Community Identification and Maintenance on Big Data Platform

“…The k-core decomposition problem in a dynamic graph was first studied in [11], and an improved alternative was introduced by Li et al in [12]. In [11], Miorandi et al provide a statistical model for contacts among vertices and compute k-core decomposition as a tool to understand the influence of a spreader in diffusion of epidemics.…”