A note on using the adjusted Rand index for link prediction in networks

• We propose the use of the adjusted Rand index to predict links in network data.
• Nine proximity measures were compared on simulated and real networks.
• The adjusted Rand index was the top performer out of the nine proximity measures considered.
• The adjusted Rand index can also be used to detect unusual or incorrect links in a network.

As network data gains popularity for research in various fields, the need for methods to predict future links or find missing links in the data increases. One subset of the methodology used to solve this problem involves creating a similarity measure between each pair of nodes in the network; unfortunately, these methods can be shown to have arbitrary cutoffs and poor performance. To address these shortcomings, we use the adjusted Rand index to create a similarity measure between nodes that has a natural threshold of zero. The effectiveness of this method is then compared to a number of other similarity measures and assessed on a variety of simulated data sets with block model structure and three real network data sets. Under this particular formulation of the adjusted Rand index, information is also provided on dissimilarity. As such, we then go on to test its use for detecting incorrect links in network data, highlighting the dual use of the approach.