  We investigate transition to synchrony in degree-frequency correlated
Sakaguchi-Kuramoto (SK) model on complex networks both analytically and
numerically. We analytically derive self-consistent equations for group angular
velocity and order parameter for the model in the thermodynamic limit. Using
the self-consistent equations we investigate transition to synchronization in
SK model on uncorrelated scale-free (SF) and Erd\H{o}s-R\'enyi (ER) networks in
detail. Depending on the degree distribution exponent ($\gamma$) of SF networks
and phase-frustration parameter, the population undergoes from first order
transition (explosive synchronization (ES)) to second order transition and vice
versa. In ER networks transition is always second order irrespective of the
phase-lag parameter. We observe that the critical coupling strength for the
onset of synchronization is decreased by phase-frustration parameter in case of
SF network where as in ER network, the phase-frustration delays the onset of
synchronization. Extensive numerical simulations using SF and ER networks are
performed to validate the analytical results. An analytical expression of
critical coupling strength for the onset of synchronization is also derived
from the self consistent equations considering the vanishing order parameter
limit.
