  Networks arise in many applications, such as in the analysis of text
documents, social interactions and brain activity. We develop a general
framework for extrinsic statistical analysis of samples of networks, motivated
by networks representing text documents in corpus linguistics. We identify
networks with their graph Laplacian matrices, for which we define metrics,
embeddings, tangent spaces, and a projection from Euclidean space to the space
of graph Laplacians. This framework provides a way of computing means,
performing principal component analysis and regression, and carrying out
hypothesis tests, such as for testing for equality of means between two samples
of networks. We apply the methodology to the set of novels by Jane Austen and
Charles Dickens.
