ABSTRACT
There are advantages to modelling connections between nodes in a social network as edges of qualitatively different types. Experiments with social groups have shown that relationships are rarely symmetric. However, the adjacency matrix is now no longer symmetric. The spectral embedding technique used so far requires that the adjacency matrix, and so the Laplacian derived from it, are symmetric. A layer approach handles directed graphs. The conventional way to embed directed graphs is due to Chung. Chung's approach represents a well-motivated way to compute a symmetric Laplacian from an asymmetric adjacency matrix. For most matrices, the "Google trick" has to be used to address reducibility, which in turn makes the matrices dense, with substantial performance costs; and as a result it tends to fold peripheral nodes inwards in the embedding, creating a misleading impression of their importance. The computations for the directed edge model approach can be done using singular value decomposition (SVD).
