Some Math background

• The normalized Laplacian of the graph G is the matrix L(G) defined as followed:

1 if u=v and dv?0,

L(G) (u, v) = -(du+dv)-1/2 if u and v are adj.

0 otherwise

• The normalized Laplacian spectrum (nls) is the set of eigenvalues of L(G), i.e., all values ? such that

L(G)*u = ?*u for some u?Rn, u?0

• Multiplicity of eigenvalue a equals to how many of the n eigenvalues are a

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