I would suggest you the article

"Using graph theory to analyze biological networks"

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3101653/ 

My suggestion would be to go to http://www.ncbi.nlm.nih.gov, select Pubmed in the drop down menu next to the search field, and then type in a query like

"biological networks" AND "graph theory"

Thank you sir.. I could find some useful articles from the website you mentioned. I am searching for some more articles on applications of graph theory to food webs.

Roberts, Fred S.

Applications of combinatorics and graph theory to the biological and social sciences.

(The IMA volumes in mathematics and its applications; v. 17) 1989 by Springer-Verlag New York Inc.

IN CONTENTS:

Applications of Combinatorics and Graph Theory to the

Biological and Social Sciences:

Seven Fundamental Ideas ...................................... .1

Fred S. Roberts

Food Webs, Competition Graphs, Competition-Common

Enemy Graphs and Niche Graphs ............................... 221

J. Richard Lundgren

If you do not have access to a citation index, I would suggest you use Google scholar. Start with the Lundgren paper that Wiwat lists and use the cited by links to look for papers.

I would suggest you the article

"Using graph theory to analyze biological networks"

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3101653/ 

Look up Jeff Dambacher's article in The American Naturalist, " Qualitative stability and ambiguity in model ecosystems". He uses basic flow graphs to construct matrices which he uses to explore the dynamics the system is likely to exhibit.  This approachhas been used in scoping and planning large simulation models of human/ecosystem interactions in Australia.  He has published a number of papers along these lines.

Perhaps this: https://www.researchgate.net/publication/239328836_A_Graph_Theory_Approach_to_Demographic_Loop_Analysis

And then there is the theory of branching processes to investigate growth and extinction of species. Here is a classic book: 

http://www.cambridge.org/ca/academic/subjects/life-sciences/evolutionary-biology/branching-processes-variation-growth-and-extinction-populations#contentsTabAnchor

And this, from Nature: 

http://www.nature.com/nrg/journal/v4/n7/glossary/nrg1112.html

And I am sure there is more! :-)

Article A Graph Theory Approach to Demographic Loop Analysis

Why not search immediately for Applications of graph theory in Kabbalistic and Talismanic networks? There are also ancient networks e.g. the Pythagorean order or the order of the Essenes or the Pharisees or any medieval craftsmens guild or Freemasons. Those networks are more related to transmission of central mysteries of the universe than really dealing with social issues of human society. The problem is that pure knowledge is not so readily available, thus you have to trace back in history, geography, bible, different law codices in order to achieve gnosis. Maybe this is what networking is all about: Building models until you achieve at a greater truth and a more useful symbol and then maybe even abandoning your network for further development.

Dear @Sudev, please do find a list attached with over 1.000 matching publications found in Research Gate data base regarding graph applications to biological networks. I know that you will have to dig papers, but there are many good resources! Regards, hope it will be helpful!

The example of one paper from the list is attached!

https://www.researchgate.net/publicliterature.PublicLiterature.search.html?type=keyword&search-keyword=graph+applications+for+biological+networks

Article MCF: A tool to find multi-scale community profiles in biolog...

Thank you so much Professor Ljubomir Jacić, I will go through that.