We investigate the characteristics of the solar flare complex network. The limited predictability, nonlinearity, and self-organized criticality of the flares allow us to study systems of flares in the field of the complex systems. Both the occurrence time and the location of flares detected from 2006 January 1 to 2016 July 21 are used to design the growing flares network. The solar surface is divided into cells with equal areas. The cells, which include flares, are considered nodes of the network. The related links are equivalent to sympathetic flaring. The extracted features demonstrate that the network of flares follows quantitative measures of complexity. The power-law nature of the connectivity distribution with a degree exponent greater than three reveals that flares form a scale-free and small-world network. A large value for the clustering coefficient, a small characteristic path length, and a slow change of the diameter are all characteristics of the flares network. We show that the degree correlation of the flares network has the characteristics of a disassortative network. About 11% of the large energetic flares (M and X types in GOES classification) that occurred in the network hubs cover 3% of the solar surface.