EDGES -- as well as VERTICES -- are IMPORTANT!

G. H. Hardy (1877-1947) was a prominent English mathematician, well-known to mathematicians for his achievements in analysis and number theory -- and for his mentorship of the Indian mathematician, Srinivasa Ramanajuan.  For most people outside of mathematics, Hardy is better known for his 1940 expository essay, A Mathematician's Apology; here are Hardy's opening sentences:

Hardy's book is often praised for its communication of the nature and beauty of mathematics but, as a long-time teacher of mathematics, I am very much in disagreement with that opening paragraph which ends with these words: " . . . there is no scorn more profound, or on the whole, more justifiable than that of the men who make for the men who explain.  Exposition, criticism, appreciation, is work for second-rate minds."

ENLARGE the view expressed by G. H. Hardy

(and his followers)

      The network of mathematicians, as I know it, reminds me of a graph -- a connected collection of edges and vertices in which the vertices represent those mathematicians whose work focuses on mathematics, itself -- discovering and verifying important ideas and relationships.  Some of the rest of us qualify better as edges -- for we study mathematics, learning what others have discovered, and connect and communicate these ideas via writing and teaching.  

from Wikipedia

Without communicators, 
mathematics is not known --
and, therefore, not as useful
as we
need it
to be.