NIMBLECORE: A Space-efficient External Memory Algorithm for Estimating Core Numbers

We address the problem of estimating core numbers of nodes by reading edges of a large graph stored in external memory. The core number of a node is the highest k-core in which the node participates. Core numbers are useful in many graph mining tasks, especially ones that involve finding communities of nodes, influential spreaders and dense subgraphs. Large graphs often do not fit on the memory of a single machine. Existing external memory solutions do not give bounds on the required space. In practice, existing solutions also do not scale with the size of the graph. We propose Nimble Core, an iterative external-memory algorithm, which estimates core numbers of nodes using O(n log d(max)) space, where n is the number of nodes and d(max) is the maximum node-degree in the graph. We also show that Nimble Core requires O (n) space for graphs with power-law degree distributions. Experiments on forty-eight large graphs from various domains demonstrate that Nimble Core gives space savings up to 60X, while accurately estimating core numbers with average relative error less than 2.3%.