Adamic–Adar index

The Adamic–Adar index is a measure introduced in 2003 by Lada Adamic and Eytan Adar to predict links in a social network, according to the amount of shared links between two nodes. It is defined as the sum of the inverse logarithmic degree centrality of the neighbours shared by the two nodes

$$A(x,y)=\sum _{u\in N(x)\cap N(y)}{\frac {1}{\log {|N(u)|}}}$$

where $N(u)$ is the set of nodes adjacent to $u$. The definition is based on the concept that common elements with very large neighbourhoods are less significant when predicting a connection between two nodes compared with elements shared between a small number of nodes.

Further reading

• Adamic, Lada A; Adar, Eytan (2003). "Friends and neighbors on the web". Social Networks. 25 (3). Elsevier: 211–230. doi:10.1016/S0378-8733(03)00009-1. S2CID 2262951.
• Barbier, Geoffrey; Pritam Gundecha, Zhuo Feng (2013). Provenance Data in Social Media. Morgan & Claypool Publishers. ISBN 9781608457847.
• Schall, Daniel (2015). Social Network-Based Recommender Systems. Springer. p. 12. ISBN 9783319227351.
• Virinchi, Srinivas; Mitra, Pabitra (2016). Link Prediction in Social Networks: Role of Power Law Distribution. Springer Briefs in Computer Science. Springer. p. 7. ISBN 9783319289229.