Do the NP: find the largest clique
Mathematica, 34 bytes

Tr[1^#&amp;@@FindClique[#&lt;-&gt;#2&amp;@@@#]]&amp;  


Basically FindClique does the job and "finds a largest clique in the graph g."
All the other stuff is converting input-list into graph 

Input


  [{{2, 5}, {2, 3}, {4, 17}, {1, 3}, {7, 13}, {5, 3}, {4, 3}, {4, 
     1}, {1, 5}, {5, 4}}]


Output


  4 


Input


  [{{1296, 316}, {1650, 316}, {1296, 1650}, {1296, 52}, {1650, 
     711}, {711, 316}, {1650, 52}, {52, 711}, {1296, 711}, {52, 
     316}, {52, 1565}, {1565, 1296}, {1565, 316}, {1650, 1565}, {1296, 
     138}, {1565, 138}, {1565, 711}, {138, 1650}, {711, 138}, {138, 
     144}, {144, 1860}, {1296, 1860}, {1860, 52}, {711, 1639}}]


Output


  6


thanx @Kelly Lowder for -10 bytes