Algorithms for Sparse Graphs. An undirected graph G is a pair (V,E), where V is a finite set of points called vertices and E is a finite set of edges.

1. Graph

2. Determine the degree of all nodes:
What is the degree of e?

3. Solution
• A special case is a loop, which adds two to the degree. This can be understood by letting each connection of the loop edge count as its own adjacent vertex. In
other words, a vertex with a loop "sees" itself as an adjacent vertex from both ends of the edge thus adding two, not one, to the degree.
• For a directed graph, a loop adds one to the in degree and one to the out degree

4. Some definitions

5. Regular Graph

6. Complete Graph

7. Planer Graph
• In graph theory, a planar graph is a graph that can be
embedded in the plane, i.e., it can be drawn in such a way
that no edges cross each other.

8. More planer graphs

9. Is this a planar graph?

10. Distance & Diameter

11. Path
• A path is a sequence of edges that begins at a
vertex of a graph and travels from vertex to
vertex along edges of the graph.