If you are referring to ego networks (the connections between your immediate connections), the visualization gets part way there. If you hover over a node, it pops up a character bio. If you click a node, it shows the immediate peer connections, but it does not go to the next step and show the connections between the people you are connected to. Analytically, that is a great social network analysis concept, since you can determine the balanced triads and determine what needs to happen to either unbalance a network (and cause the relationships to unravel) or balance a network and make it stable.