Which similarity measure to use in network analysis: Impact of sample size on phi correlation coefficient and Ochiai index

Some networks are explicit where members make direct connections (e.g. Facebook network), whereas other networks are implicit (e.g. co-citation network) in which an edge between two nodes is inferred using a similarity index. Choosing the right index to infer connections in an implicit/inferred network is important because conclusions can be biased if a network does not represent true relationships. In this study, we compared two indexes: Phi Correlation Coefficient (PCC) and Ochiai Coefficient (Och) based on their sensitivity to the sample size of transactions from where the network is inferred. For demonstration, we used an implicit network, called a comorbidity network, developed from health records of 22.1 million patients. The networks were compared based on their overall topologies and node centralities. Results showed that the network formed using Och was more robust to the sample size than PCC. The network using Och followed a small-world topology irrespective of the sample size whereas the structure of a network using PCC was inconsistent. Regarding node centralities, the betweenness centrality was most affected by the sample size. Our results lead us to recommend Och over PCC.