Cliques influence on the spectrum of normal modes vibration in complex networks

The collective vibrations in systems of linearly coupled oscillators has served as a simple paradigmatic model of collective phenomena. It is of particular recent interest, the case when the arrangement of the oscillators is not periodic, as is in the context of lattice vibrations of a crystalline solid, but when they lie on a complex network. In this work, the influence of the network-cliques number on the collective vibrations of linearly coupled oscillators is investigated for particular network topologies. Namely, we start with fully connected tree networks (no cliques) and different degree distributions. Then we systematically add higher order cliques to these trees to analyze their effect on the frequency spectrum.