Efficient analytical computation of expected frequency of motifs of small size by marginalization in uncertain network

Counting motifs in an uncertain graph for which each link is associated with a connection probability is computationally expensive when the graph is huge due to the extremely large number of possible worlds. Natural approach is to rely on sampling-based approximation methods, but this still needs many sample graphs for obtaining accurate results. We propose a novel method that analytically computes the expected frequency of motif without relying on expensive sampling. Marginalizing the probability of each possible world on a candidate motif can drastically reduce the number of possible worlds that need be considered when the size of motif is small. Experiments using real-world data confirm that the proposed method is effective and efficient. It is far better than the state-of-the-art sampling-based method. The accuracy is guaranteed and the running time is about 4 order of magnitude faster. It runs at a speed that does not depend on the connection probability.