Fig. 2: Structural network measures.

a Neighbourhood of motif M₁ (Fig. 1) and its adjacency matrix. Network and matrix representation of two structural (full, respectively sparse) network measures, b the exponential matrix (a measure of vertex communicability³⁷), and c the graph Laplacian. In each case, the vertices are numbered 1 to 5 and coloured by orbit, and a non-zero (i, j)-entry in the matrix corresponds to the edge weight between vertices i and j. Note that the network automorphism swapping vertices 1 and 2, and 3 and 4, preserves the network and matrix structure in all three cases. In general, any symmetry of a network is also a symmetry of the network representation of any structural network measure.