  The problem of community detection is important as it helps in understanding
the spread of information in a social network. All real complex networks have
an inbuilt structure which captures and characterizes the network dynamics
between its nodes. Linkages are more likely to form between similar nodes,
leading to the formation of some community structure which characterizes the
network dynamic. The more friends they have in common, the more the influence
that each person can exercise on the other.
  We propose a disjoint community detection algorithm, $\textit{NashDisjoint}$
that detects disjoint communities in any given network. We evaluate the
algorithm $\textit{NashDisjoint}$ on the standard LFR benchmarks, and we find
that our algorithm works at least as good as that of the state of the art
algorithms for the mixing factors less than 0.55 in all the cases. We propose
an overlapping community detection algorithm $\textit{NashOverlap}$ to detect
the overlapping communities in any given network. We evaluate the algorithm
$\textit{NashOverlap}$ on the standard LFR benchmarks and we find that our
algorithm works far better than the state of the art algorithms in around 152
different scenarios, generated by varying the number of nodes, mixing factor
and overlapping membership.
  We run our algorithm $\textit{NashOverlap}$ on DBLP dataset to detect the
large collaboration groups and found very interesting results. Also, these
results of our algorithm on DBLP collaboration network are compared with the
results of the $\textit{COPRA}$ algorithm and $\textit{OSLOM}$.
