A revisit to evaluating accuracy of community detection using the normalized mutual information

Normalized Mutual Information (NMI) has been widely used to evaluate accuracy of community detection algorithms. In this notes we show that NMI is seriously affected by systematic error due to finite size of networks, and may give wrong estimate of performance of algorithms in some cases. A simple expression for the estimate of this error is derived and tested numerically. We suggest to use a new measure to accuracy of community detection, namely relative Normalized Mutual Information (rNMI), which is NMI minus the expected NMI of random partitions. This measure is very close to zero for two random partitions even with a short length, so it can overcome the problem of NMI.