Complete Graph & Connected Component There seems to be various implementations of algorithms that find the connected components of a graph. 

I have not found, however, an algorithm or implementation for finding which of the connected components are also complete. Does anybody know of one?

Thank you!
Most graph libraries will find the connected components of a graph G as a list of connected subgraphs [H1, H2, H3, ...] and most of these libraries will have the functionality to obtain the number of nodes and number of edges in a graph. Assuming H is a simple graph (no loops, no multiple edges) with m edges and n vertices, one can say it is complete if

m == n*(n-1)/2


So, given the output of connected components, you should do:

for each graph H in [H1, H2, ...]
  int n = H.getNumVertices()
  int m = H.getNumEdges()
  if (n*(n-1) == 2*m)
    state that H is complete
  else
    state that H is not complete