What algorithms can I use to make inferences from a graph?

Question

Edited question to make it a bit more specific.

Not trying to base it on content of nodes but solely of structure of directed graph.

For example, pagerank(at first) solely used the link structure(directed graph) to make inferences on what was more relevant. I'm not totally sure, but I think Elo(chess ranking) does something simlair to rank players(although it adds scores also).

I'm using python's networkx package but right now I just want to understand any algorithms that accomplish this.

Thanks!

Answer 1

Eigenvector centrality is a network metric that can be used to model the probability that a node will be encountered in a random walk. It factors in not only the number of edges that a node has but also the number of edges the nodes it connects to have and onward with the edges that the nodes connected to its connected nodes have and so on. It can be implemented with a random walk which is how Google's PageRank algorithm works.

That said, the field of network analysis is broad and continues to develop with new and interesting research. The way you ask the question implies that you might have a different impression. Perhaps start by looking over the three links I included here and see if that gets you started and then follow up with more specific questions.

Answer 2

You should probably take a look at Markov Random Fields and Conditional Random Fields . Perhaps the closest thing similar to what you're describing is a Bayesian Network