I am working on a research project that deals with social networks. I have done most of the backbone of the program in C++ and am now wanting to implement a way to create the graph of nodes and the connections as well as a way to visualize the connections between people. I have looked a little into Lemon and the Boost graph library, but was wondering which one would be easier to learn and implement or if I should just code my own.
Methods for implementing and using graphs of nodes in C++?
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If you use the BGL then you should also be able to make use of the Graph Toolkit for Algorithms and Drawings (GTAD). The GTAD is meant to be compatible with BGL and adds a number of graph algorithms not in BGL as well as algorithms for layouts.
For visualization the BGL allows you to read and write some common graph file types such as GraphML and Dot for use with GraphViz.
Lemon looks to be a well featured library with a good array of algorithms. You can also use gLemon to view Lemon graphs. This visualizer looks quite basic though and was last updated in 2008, unlike Lemon which is still under development.
I would suggest you first work out what you want to do with any graphs you create, ie what algorithms you require (shortest-path etc) and compare the two libraries from that respect.
Also take a look at the tutorials for both. They have very good documentation and should help you decide which you'll find easier to implement.
Unless you really want to get into the details of how certain graph structures and algorithms are implemented I would use a library.