  We derive exact equations for the spectral density of sparse networks with an
arbitrary distribution of the number of single edges and triangles per node.
These equations enable a systematic investigation of the effect of clustering
on the spectral properties of the network adjacency matrix. In the case of
heterogeneous networks, we demonstrate that the spectral density becomes more
symmetric as the fluctuations in the triangle-degree sequence increase. This
phenomenon is explained by the small clustering coefficient of networks with a
large variance of the triangle-degree distribution. In the homogeneous case of
regular clustered networks, we find that both perturbative and non-perturbative
approximations fail to predict the spectral density in the high-connectivity
limit. This suggests that traditional large-degree approximations may be
ineffective in studying the spectral properties of networks with more complex
motifs. Our theoretical results are fully confirmed by numerical
diagonalizations of finite adjacency matrices.
