title: Largest number of edges IF graph has more than one connected component
body: <p>For a algorithms final review, this question came up:</p>
  
  <pre><code>For a Graph G with V vertices and E edges, what is the largest number of edges 
  this graph can have IF there are more than one connected components within G
  </code></pre>
  
  <p>Since a connected component is essentially a graph within a graph, that means all vertices within the subgraph must be removed from the larger graph while remaining internally connective.  I can understand the intuition, but am having a hard time converting it into a formula.</p>
  
  <p>Here's what I've come up with so far:</p>
  
  <p>For connected component n, each graph Gn has a corresponding vertex set {Vn} such that the contents of the vertex set are internally connected, while remaining externally disconnected.</p>
  
  <pre><code>Graph G1 = {V1}
  Graph G2 = {V2}
      ...
  Graph Gn = {Vn}
  </code></pre>
  
  <p>Now, each {Vn} contains a maximum of V * (V-1) edges.  </p>
  
  <p>How can I express the maximum number of edges using a formula?</p>