Network Analysis: Intra-Individual Covariance Network and Graph Theory Approach

Intra-individual covariance depicts inter-item similarities and differences within each individual to determine the variance from the group-averaged value of each item. In the current study, intra-individual covariance between two different items was defined using the following formula: 1e((xA-MA)SDA-(xB-MB)SDB)2. Thus, the intra-individual covariance value could be distributed between 0 and 1, where higher values indicate greater similarity in degrees of variance [= differences between raw values (X_A and X_B) and group-averaged values (M_A and M_B, n = 454) divided by the group-level standard deviation of each item (SD_A and SD_B, n = 454)] between the two items of A and B within an individual (31, 32). By calculating these intra-individual covariance values among the 43 variables described above within each individual, intra-individual covariance networks were constructed for each individual (n = 454).

To uncover the principal influences on medical students' daily lives during the COVID-19 pandemic among these 43 variables, the current study applied the graph theory approach to these intra-individual covariance networks. First, network connectedness, small-worldness (σ, degree of balance between the overall network integration vs. network segregation into distinctive subgroups), and modularity (Q, heuristically estimated degree for a network to be subdivided into clearly delineated and non-overlapping subgroups) were derived using the network density range of K = 0.05–0.20 (with intervals of 0.1; when K = 0.05, only the top 5% largest values of intra-individual covariance survived as edges comprising an intra-individual covariance network). Second, a local network metric, known as betweenness centrality values (variable with higher betweenness centrality might be a “shortcut” among a larger number of variables that showed similar degrees of variance from group-averages within an individual), was estimated at the most sparse level of network density (K) that satisfies (1) network connectedness (>80% of items connected to each other, because they have similar degrees of variance from the group-averaged values of each variable), (2) small-world organization (σ > 1), and (3) modularity (Q > 0.3) for > 95% of participants (n = 454). These values were rank-transformed within each individual. All graph theory processing was conducted using the Brain Connectivity Toolbox (33).