## Graphs

A graph is simply a structure consisting of “edges” and “vertices.” An edge will connect two vertices together, and if appropriate, the edge may be defined as directed to indicate a proper direction. It is possible to have multiple edges between the same two vertices, which we call an instance of “multiple edges” --- the graph would be classified as a “multigraph.” Cycles in graphs are paths that can be taken along edges that start and end at the same vertex. A “1-cycle,” also called a “loop,” is an edge that connects a vertex to itself. A “2-cycle” is a cycle that consists of two edges, and an “n-cycle” consists of n edges.

This paper will be mostly concerned with “quivers,” which are a particular type of “directed multigraph” (a graph consisting of directed edges, which also allow for multiple edges). A quiver is special in that it strictly prohibits any instances of 1-cycles and 2-cycles.