  We introduce the multineighbor complex of a graph, which is a simplicial
complex in which a simplex is a subset of the graph with a sufficient number of
mutual neighbors. We investigate the asymptotic homological properties of such
complexes for the Erdos-Renyi random graphs and obtain a number of vanishing
and nonvanishing results. We use this construction to perform a topological
data analysis classification of noisy synthetic point clouds obtaining
favorable accuracy as obtained by the standard methods. The case when there is
a single neighbor has been studied earlier by Mathew Kahle.
