Leonhard Euler,
the eighteen century Swiss mathematician, who is often called the father of graph theory.

(from http://www2.physics.umd.edu/~redish/Money/euler.jpg)

The map of Konigsberg in the eighteenth century, showing the river and the seven bridges that inspired Euler to introduce the first graph, creating graph theory.

A map of Kaliningrad today,  rebuilt after its destruction in World War II.

(from http://www-groups.dcs.st-andrews.ac.uk/~history/Miscellaneous/Konigsberg.html)
 

Paul Erdös
perhaps the most prolific mathematician of all times. For his biography, see http://turnbull.dcs.st-and.ac.uk/~history/Mathematicians/Erdos.html 

(from http://www.ams.org/new-in-math/erdosphoto.html)

Two recent biographies of Paul Erdos.

Alfréd Rényi
who together with Paul Erdos founded the theory of random networks. For his biography, see http://turnbull.dcs.st-and.ac.uk/~history/Mathematicians/Renyi.html

(from http://www.gabay.com/sources/Liste_Bio.asp?NP=RENYI+Alfred)
 

Bela Bollobas,
Erdos's student and close collaborator, at Notre Dame, making a point to the author about scale-free networks. Bollobas proved in 1982 that random networks have a Poisson degree distribution.