A simple embedding for classifying networks with a few graphlets

Complex networks are a key analytical tool for complex systems. However if one wants to apply this tool in machine learning applications where the data is non-relational data one must find an appropriate network embedding. The embedding represents a network in a vector space, while preserving information about network structure. In this paper, we propose a simple network embedding technique that avoids the need for graph kernels or convolutional networks, as have previously been advocated. Our embedding is based on 3-node and 4-node graphlet counts combined with some feature extraction based on a Principal Component Analysis (PCA). We show that it is competitive with some state-of-the-art methods on a downstream classification task. We then show how to reduce the computational effort in the method by transforming extraction into a feature selection procedure. We claim that this selection procedure, a generalisation of PCA, is more meaningful than a popular alternative.