Reading through "40 algorithms every programmer should know"
This isn't explained very clearly Function for determining fraud in a graph network
For some clarity this is around graph theory and trying to determine if a vertex/node, representing a person in a network of people they know, is part of a set representing fraudulent activity.
Here is how it's explained in the book. "If we want to find the probability that a certain node, a, belongs to F, the probability is represented by P(F/q) and is calculated as follows: (image above)
Let's apply this to the preceding figure, where Neighborhoodn represents the neighborhood of vertex n and w(n, nj) represents the weight of the connection between n and nj. Also, degreeq is the degree of node q."
This doesn't make clear to me what F and q mean as the inputs in P(F/q). Does this mean F is a set, and q is an element of that set? Or does this mean the input is some ratio of connectivity? Edit: I see this is probably meaning conditional probability.
I'm also not sure what class(nj)=F means. The usage of the word class throws me off. I don't know if F is in reference to the set of fraudulent nodes, or if this is stating that F is the fraud value of the neighboring node.
Or what w(n, nj)DOSnormalizedj means. I understand that this is some weighted relationship of the node in question with it's edges. I've never seen DOSnormalized before. Does this mean we total all the weights and normalize them by the degree or edge count? Looks like DOS is density of state?
Thanks a bunch for any help with this!