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Analysis and modeling of networked objects are fundamental pieces of moderndata mining. Most real-world networks, from biological to social ones, areknown to have common structural properties. These properties allow us to modelthe growth processes of networks and to develop useful algorithms. Oneremarkable example is the fractality of networks, which suggests theself-similar organization of global network structure. To determine thefractality of a network, we need to solve the so-called box-covering problem,where preceding algorithms are not feasible for large-scale networks. The lackof an efficient algorithm prevents us from investigating the fractal nature oflarge-scale networks. To overcome this issue, we propose a new box-coveringalgorithm based on recently emerging sketching techniques. We theoreticallyshow that it works in near-linear time with a guarantee of solution accuracy.In experiments, we have confirmed that the algorithm enables us to study thefractality of million-scale networks for the first time. We have observed thatits outputs are sufficiently accurate and that its time and space requirementsare orders of magnitude smaller than those of previous algorithms.

Fractality of Massive Graphs: Scalable Analysis with Sketch-Based Box-Covering Algorithm