title: Formula for the maximum possible number of 3-cliques (triangles) in an undirected graph
body: <p>As the question states. I seem to be unable to figure out the formula that corresponds to the paper &amp; pencil results. I am looking for a formula to give me the maximum possible number of triangles in an UNDIRECTED graph.</p>
  
  <p>A triangles is defined as any connection of nodes of path length 3 that forms a cycle. e.g If I have a graph with 1&lt;->2&lt;->3&lt;->1 is a triangle(&lt;-> is an undirected connection). If what a triangle is is unclear the top of page 2 has a figure showing what a triangle is in this context <a href="http://arxiv.org/pdf/1202.5230v1.pdf" rel="nofollow">http://arxiv.org/pdf/1202.5230v1.pdf</a>.</p>
  
  <p>Thanks</p>