In the alpha-band, the networks of BD patients had increased L and decreased C and Eg as a function of connection density (all p < 0.05 with permutation tests). The findings were broadly preserved over a range of thresholds corresponding to connection density of 5–100% (Fig. 5). Because the networks are almost sparsely connected with the highest SL values for a lower threshold of connection density, the corresponding network measures are likely to have the minimum. As the connection density increased, more edges were added into the graphs and the network measures were rapidly increased. Then, beyond the threshold of the Erdös–Rényi model (Erdös and Rényi, 1961), which predicts that most of nodes are fully connected, the network measures tended to converge. SL networks of BD patients showed no significant changes in γ, λ, and σ, which suggest that the networks of BD patients and controls have the same small-world organization for the functional brain network. Also, in other frequency bands, there were no significant changes of global network measures over all thresholds of connection density.
