Expander graphs are highly connected and sparse graphs that have a lot of applications in networks and computers. This property over a graph is equal to another property over a matrix related to the graph. In this dissertation, we explain two different ways to construct an infinite family of expander graphs. One uses Kazhdan property on a family of groups and gives us Cayley graphs which are expander. Another way family of expanders can be constructed is by induction and graph products. We extend the definition of an expander for hypergraphs. We also have conjectures that develop those constructions for an infinite family of expander hypergraphs close to those approaches we have for expander graphs.
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