1. Graphs with more than 2 nodes can sometimes have emergent properties in their subgraphs:

   Definition: A subgraph of a graph is a graph whose vertex set and edge set are subsets of those of . If is a subgraph of , then is said to be a supergraph of

   Given this definition and the above point about emergent properties, find the following: a.How many triangles are there in the above graph? A triangle is a graph pattern where there is a 3 node cycle. b.How many rectangles are in the graph? A rectangle is a graph pattern with a 4 node cycle. c.Do you think that there is an algorithmic way to try to find the number of triangles in a graph? Try to write up a series of pseudocode steps to do so.