Exceptional books on real world applications of graph theory.
I highly recommend: Graph Theory and Its Applications to Problems of Society by Fred S. Roberts, Series: CBMS-NSF Regional Conference Series in Applied Mathematics(No. 29),ISBN:9780898710267, 1987.
This book is extremely well written and despite the fact that it dates back over 20 years surveys applications of graph theory to assigning directions to streets, routing problems, scheduling questions, etc.
There is an area of very active research that has direct connections with the graph theory: I am talking about what is commonly called the network science. It usually includes statistical analysis of real world networks, random graph theory as a null model, dynamical processes on random graphs such as percolation or epidemic spread, and mathematical models of network formation.
Two recent books that both heavy on the theory and applications are
- Networks: An introduction by Mark Newman
- Social and Economic Networks by Matthew Jackson
The first book is slightly more theoretical in nature and includes a lot of derivation of simple results. It also has quite a detailed discussion of real world networks. The second book is more oriented to the description of various social, economic, etc situations where network analysis allows to make some conclusions.
I would like to mention another nice book about the applications of graph theory, which though I don't think it has all of the virtues of Fred Roberts' book Graph Theory and its Applications to Society, already mentioned, is none-the-less worth a look. The book is: Applications of Graph Theory, editors, Robin Wilson and Lowell Beineke. The book was published by Academic Press in 1979. Its age makes it somewhat "dated" but it still has some rather nice things. Chapters include Graph Theory and Communications Networks (definitely dated), Graph Theory and Electrical Networks, Chemical Applications of Graph Theory, Graph Theory and Operations Research, Graph Theory and Geography, Graph Theory and the Social Sciences (written by Fred Roberts), Architectural Applications of Graph Theory, Graph Theory and Lingistics, etc. (There are total of 13 independent chapters.)