Robustness analysis of partially interdependent networks with different coupling preferences and multicluster functional nodes in VCMS

•Increasing qAB between subnetworks drops their robustness and results in a change of a second to first order phase transition.•0 ≤ q ≤ qmin causes a continuous collapse. q ∈ [qmin, qmax] causes a hybrid transition and 1 ≥ q ≥ qmax causes a discontinuous one.•With the same qAB or the same q, an WS-BA coupled network is more vulnerable than BA-BA one, while more robust than WS-WS one.