Practical algorithms for triangle computations in very large ( sparse ( power-law ) ) graphs

Finding, counting and/or listing triangles in large graphs are natural problems, which received recently much attention because of their importance in complex network analysis. However, the time and/or space requirements of known algorithms limit our ability to solve these problems in practice. We give here a quick overview of previous results, with a special emphasis on space requirements, which were not considered before. We then detail the analysis a recently proposed algorithm which surpasses all previous ones. We propose an improvement of this algorithm that significantly reduces its space requirements, as well as a new algorithm with similar performances. These two algorithms have the additional advantage of performing better on power-law graphs, which we also study. This explains their high efficiency observed in practice. They both make it possible to practically solve triangle problems in cases that were previously out of reach, which we illustrate with a typical example.

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