We investigate combustion dynamics using complex networks. We observed a transition from low-amplitude, aperiodic, combustion noise to high-amplitude, periodic, thermoacoustic instability via intermittency in the system dynamics of a turbulent lifted jet flame combustor while varying the location of the burner inside the combustor. As we change the burner location further past the condition of thermoacoustic instability, intermittency is again observed and finally, the flame blows out. The complex networks are derived from the time series data of acoustic pressure which represent the system dynamics using the visibility algorithm. We show that time series data of acoustic pressure during combustion noise exhibit a scale-free behavior. The scale-free nature of combustion dynamics disappears at the onset of thermoacoustic instability. We show that the system dynamics during thermoacoustic instability can be represented as a regular network. Further, we show that the transition from thermoacoustic instability to flame blowout is reflected as a transition from regular to scale-free structure in the topology of the complex network. The use of complex networks help to formulate the pattern emerging during the transition in combustion dynamics. These structural changes in topology of the complex networks are quantified by calculating the network properties. We propose these network properties as early warning precursosrs to detect the onset of impending thermoacoustic instability and blowout. © 2015, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.