Simple Graph: unique connections, no reflexive connections Multigraphs: multiple connections between two vertices permitted Directed graphs/digraph Pseudograph: permits self-links Degree of vertex in an undirected graph: edges connected to vertex (loops contribute twice) in a directed graph: in-degree is edges pointing to a vertex, out-degree is pointing out Pendant vertex has degree 1 Sum of the degree of all vertices in an undirected graphs is twice the number of edges: handshake theorem Bipartite: can be partitioned into two sets of vertices such that no edge connects two vertices in the same set Complete bipartite: two vertices are connected \iff they are in seperate partitions Matching in a bipartite graph: find a subgraph such that all vertices have *exactly* 1 edge attached