Abstract: This paper investigates the influence of average degree and scale of network on the partial synchronization state of the complex networks. The research results show that average degree may have effects only when the networks are in partial synchronization states, whether the network model is random network, small-world network or uncorrelated configuration network. Increasing the average degree can improve the partial synchronization state for the three network models. However, this can make the complexity change in completely different ways at different coupling strength regions. As to the network scale, it may have effects on small coupling strength: increasing the network scale may worsen the synchronization state and decrease the complexity. For the nearest-neighbor network, with the increase of average degree, the synchronization state of the whole network may be better and the complexity may be larger; and with the increase of network scale, the synchronization state of the whole network may be worse and the complexity may be smaller. This research makes the partial synchronization state clearer and proposes useful suggestions for the construction of multi-function networks.

Key words: complex networks, average degree, network scale, partial synchronization