On the Combinatorial Energy of the Weisfeiler-Lehman Algorithm
Authors: Martin Fürer
Summary: The classical Weisfeiler-Lehman methodology WL[2] makes use of edge colours to supply a robust graph invariant. It’s at the least as highly effective in its means to differentiate non-isomorphic graphs as essentially the most outstanding algebraic graph invariants. It determines not solely the spectrum of a graph, and the angles between customary foundation vectors and the eigenspaces, however even the angles between projections of normal foundation vectors into the eigenspaces. Right here, we examine the combinatorial energy of WL[2]. For sufficiently massive ok, WL[k] determines all combinatorial properties of a graph. Many historically used combinatorial invariants are decided by WL[k] for small ok. We concentrate on two elementary invariants, the num- ber of cycles Cp of size p, and the variety of cliques Kp of measurement p. We present that WL[2] determines the variety of cycles of lengths as much as 6, however not these of size 8. Additionally, WL[2] doesn’t decide the variety of 4-cliques
