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Hai I asked the same question to some researchers in Tamilnadu Anna University,I came to know that they are doing research to develop some theories neglecting the application level.Thus they can get PhD soon and using that PhD certificate they can demand better salary from self financing engineering colleges where the management treats MSc degree & ME/MTech degrees in different salary package.Using the better salary they can get married and can run a family life.Thus they applies graph theory for earning purpose.This is the ultimate real life application of Mathematics PhDs.Graph theory is an example,Real analysis is other good example:One Professor at NIT Calicut laughed at me when I enquired him the application of his PhD thesis in real life.He says that he gets good position in society ,others calls him Professor and reader.He owned Car and good villa using his PhD certificate.My advice to you is its better to develop some theories neglecting the application of what you study,then you will be considered as a good thinker having sound knowledge.You can work -teach with the PhD certificate as any poor MSc works ,but can get salary 8 times that of mere MSc.Thus you can enjoy life.This is the real applications.

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Q: What is the use of graph theory in your real world?
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