  In recent years, there has been a growing recognition that higher-order
structures are important features in real-world networks. A particular class of
structures that has gained prominence is known as a simplicial complex. Despite
their application to complex processes such as social contagion and novel
measures of centrality, not much is currently understood about the
distributional properties of these complexes in communication networks.
Furthermore, it is also an open question as to whether an established growth
model, such as scale-free network growth with triad formation, is sophisticated
enough to capture the distributional properties of simplicial complexes. In
this paper, we use empirical data on five real-world communication networks to
propose a functional form for the distributions of two important simplicial
complex structures. We also show that, while the scale-free network growth
model with triad formation captures the form of these distributions in networks
evolved using the model, the best-fit parameters are significantly different
between the real network and its simulated equivalent. An auxiliary
contribution is an empirical profile of the two simplicial complexes in these
five real-world networks.
