analogue of a graph is called a [*simplicial complex*]{}. It can be viewed as a hypergraph with a closure property, namely, for any hyperedge in the hypergraph all of its subsets are also in the hypergraph. An hyperedge of size $i$ is called an [*$(i-1)$-face*]{} of the complex. Thus, the vertices of the complex are the $0$-faces, the edges are the $1$-faces, the triangles are the $2$-faces, etc. A complex is termed [*bounded degree*]{} if the number of faces of any dimension which are incident to any vertex is bounded by a constant, independent of the number of vertices in the complex.

#### On high dimensional expanders.

The study of high dimensional expanders gains a lot of interest recently. They were proven to be a bridge between deep questions in topology (such as topological overlapping, see [@Gro10]) and important questions in theoretical computer science (such as property testing and error-correcting codes, see [@KL14]). The interested reader is referred to [@Lub14] for a recent survey on high dimensional expanders. The general hope is that high dimensional expanders could be used in places where expander graphs were not good enough.

Expander graphs have had an enormous effect on computer science. However, there 