d ( k ) is called the density of states. The right hand side of the trace formula is made up of two terms, the Weyl term L π π is the mean separation of eigenvalues and the oscillating part is a sum over all periodic orbits p = ( e 1 , e 2 , … … , e n ) on the graph. L p = ∑ ∑ e ∈ ∈ p L e is the length of the orbit and L = ∑ ∑ e ∈ ∈ E L e is the total length of the graph. For an orbit generated by repeating a shorter primitive orbit, r p counts the number of repartitions. A p = σ σ e 1 e 2 σ σ e 2 e 3 … … σ σ e n e 1 is the product of the transition amplitudes at the vertices of the graph around the orbit.