For challenges regarding graphs, mathematical structures used to model relations between objects.
Graphs are a mathematical construct consisting of a set of vertices and a set of edges that connect the nodes. Graphs are used to model a large array of real world problems and are generally used to demonstrate the relationship between different entities.
There are many variations on the simple graph that are studied in graph-theory. Examples include
Directed graphs are graphs where the edges also carry an additional piece of information indicating a direction.
Multigraphs are graphs that allow more than one edge between two vertices; and depending on the application may or may not allow an edge to connect a vertex to itself.
Weighted graphs are graphs where the edges store an additional value for the "weight" of the edge. Weight can be used to represent many things but it is often used to represent resistance or cost.
These example types can be combined into more complex graph variants. For example weighted directed graphs are used in Network flow problems.