Introducing Hypergraphs to Early College Students

The growing importance of computational science and informatics has given rise tocomplex systems which are often modeled using hypergraphs; these are generalizationsof graphs that are used in modeling phenomena in cyberspace, relations ininformation systems, social networks, etc. In this research, we explore several classesand families of hypergraphs. Two classes are considered, namely, linear and nonlinear.The former is well-studied and yet the latter is barely known. We explore andclassify various families of each class through the notions of linearity, uniformity, beingbalanced and semi-balanced along with their cyclic natures. After defining andproving some necessary conditions on the existence of some of these hypergraphs, weintroduce several activities and applied problems along with their solutions to engageearly college students on hypergraphs