Discrete Best books on algorithmic graph theory?

[Arsenic&Lace]

I constantly find new algorithmic graph theory problems that I need to solve as I work in research. I've learned bits and pieces from google'ing and reinvented the wheel on numerous occasions but it would be nice to get a more standard background. Network science might be more applicable although I don't know; there is usually quite a bit of data on the graphs themselves which is relevant for calculations. Books on network theory/algorithmic graph theory would be nice.

Thanks,
Arsenic 'n Lace

 

[micromass]

Any special algorithms you're interested in? Any special programming language that you like to be used.

My favorite book on the subject is probably this free book: https://code.google.com/p/graphbook/ But if this is what you need depends a lot on what you want to do with graphs since there is so much you can do.

Some chapters are sadly unfinished though, especially the algebraic graph theory chapter is something I'm looking forward to.

 

[Arsenic&Lace]

Looks interesting. I'm not interested in any particular algorithm, I just want to get a feel for common algorithms. I program primarily in python.

So far I've needed to work with random walks on graphs (e.g. MFPT from one cluster to another), graph clustering, metrics for quantifying network evolution, and other problems. Right at this very moment, I am examining trajectories on simple closed graphs with self edges and looking for linear algebraic techniques to quickly find certain cycles (e.g. for a 3 node network, if I have a path 0000111122222222, I want to quickly count this, and disregard a path like 1010111000110222)

EDIT: For the record, I've solved most of the above problems, but I don't know if I've reinvented the wheel, reinvented the wheel and made it worse, or reinvented the wheel and made it better (doubtful), I mainly want to see how deeply I am in unknown territory or if I just need more basic knowledge on the subject.