# Is there a metric for "cliquiness" for social graphs?

Regarding social network graphs, let us say that I am connected to 10 people, and that each of them are connected to 10 people. At one extreme this means that I have 100 unique $$2^{nd}$$ degree connections. However it is highly likely that in a real social network many of the connections of my first degree connections are following me back and following one another and following the same people outside of my direct connections. At the other extreme, if I am connected to 10 people, and each of them are connected to 10 people, my first degree connections might only be following me and one another. In this case I only have 10 unique $$2^{nd}$$ degree connections.

Here is my question, is there any metric – I do not know, "cliquiness" – that describes the degree to which people are likely to "in-follow" vs. "out-follow"? Here I am thinking that cliquiness=1.0 corresponds to my network being a fully connected, directed graph and cliquiness=0.0 means being my graph is a directed tree. I would like to look at real networks and be able to tell what their cliquiness number is. Any leads?

If you're looking at "in-follow" vs "out-follow", a simple ratio of k_in / k_out would give you an indication of "flow", i.e. whether the node is a source or a sink of traffic.