Learning Data Mining with Python

Chapter 7
As you can see, it is very well connected in the center!
This is actually a property of our method of choosing new users—we choose those
who are already well linked in our graph, so it is likely they will just make this
group larger. For social networks, generally the number of connections a user has
follows a power law. A small percentage of users have many connections, and others
have only a few. The shape of the graph is often described as having a long tail. Our
dataset doesn't follow this pattern, as we collected our data by getting friends of
users we already had.
Creating a similarity graph
Our task in this chapter is recommendation through shared friends. As mentioned
previously, our logic is that, if two users have the same friends, they are highly similar.
We could recommend one user to the other on this basis.
We are therefore going to take our existing graph (which has edges relating to
friendship) and create a new graph. The nodes are still users, but the edges are going
to be weighted edges. A weighted edge is simply an edge with a weight property.
The logic is that a higher weight indicates more similarity between the two nodes
than a lower weight. This is context-dependent. If the weights represent distance,
then the lower weights indicate more similarity.
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