Average Nearest Neighbor degree evolution operator

[ChrizZz110]

Just in the same way we can compute the degree of each node, we may be interested in the question of whether nodes in the network tend to connect to others of high degree, or whether the connections in the network occur at random, irrespective of degree. The first situation, where people tend to connect to other people of high degree is called preferential attachment in network science (Barabási and Albert 1999. It is also referred to as a popularity tournament structure in sociology (Waller 1937). If you went to a real live high school, you may know how this works.

To get a sense of whether a given node prefers to connect to others who also have a large number of connections, we can compute an index called the average nearest neighbor degree, which is conventionally written k_nn(i).

See here for further details: ANND

For temporal graphs, at each point in time, the ANND might change. We thus define the ANND Evolution for a vertex in a given time interval.