So, I am working for a social project involving graph theory. I have a dynamic dataset (weighted and undirected), I made graphs out of them ( for 10 years ). Now, I am trying to find out relations between those graphs. I basically aim to do some knowledge discovery out of those graphs that I made. I did some research and reached the following conclusion: I can compare graphs in two ways:
1.) Either I can use the similarity techniques ( Graph edit distance, or Feature extraction or iterative methods ) which basically prove if two graphs are isomorphic/subgraphs or not.
2.) I can go by the method of ego networks. I can extract a particular ego ( a node, or a group of people ) and study only their properties and their evolution about how the ego's nature changes over a period of time.
I wish to know, is there any other way of like this of doing some knowledge discovery?
PS. I sort of feel this is not the appropriate place for this question, so it will be great if you can guide me to the right forum and not actually downvote it. This problem is somewhat close to my heart as I said, I am doing it for a social cause.
I'll hazard an answer.
What to do would depend on the network and what you want to look for. Generally it's better to start with a hypothesis and test for it, rather than diving in trying to "find something interesting". I suggest you play around with it manually, e.g. try drawing the data (or parts of it) in different ways, until you find something you might be interested in specifically researching.
E.g. I studied my Facebook social network, and found that $4$-cycles tended to have "chords". I then compared this to other networks, and found that the $4$-cycles are important for determining the frequencies of other subgraphs.
Researchers often look at clusters in social networks (close nit communities); e.g. the famous Karate Club network. And with a dynamic network, look at how they change over time. (I think things like edit distance would be impractical to implement though. But it depends on the data.)
Researchers also search for network motifs (and how these change over time). Whether or not this is possible and worthwhile depends on the data.
Personally, I find a lot of network analysis dissatisfying: it's promoted as being a next big thing, but almost always only very broad statements can be made from the network structure (there's a dense cluster here, these few nodes are hubs, it is resistant to random edge failures, and so on). To get a non-superficial understanding, a careful (and time-consuming) human analysis is needed.