The problems of selecting the winner in a tournament, a leader in a society, or the most dominating or influential person in a group of individuals are not infrequent. Graph theory is successfully used in such situations in locating, by the use of associated matrices of graphs representing the individuals under the studied relation, the person with the greatest power to influence. In this paper one more important point is brought into consideration before selecting the leader or the most influencing personality—that is the consideration of weakness to be influenced by. The one with a nice blending of these two characters—possessing the highest power to influence a person and simultaneously having the least weakness to be influenced by—is to be selected. But, in practice, to locate such a man in a group is delicate. A solution is presented here by appealing to graph theoretic notions and using them.