Temporal knowledge graph (TKG) reasoning has become a hot topic due to its great value in many practical tasks. The key to TKG reasoning is modeling the structural information and evolutional patterns of the TKGs. While great efforts have been devoted to TKG reasoning, the structural and evolutional characteristics of real-world networks have not been considered. In the aspect of structure, real-world networks usually exhibit clear community structure and scale-free (long-tailed distribution) properties. In the aspect of evolution, the impact of an event decays with the time elapsing. In this paper, we propose a novel TKG reasoning model called Hawkes process-based Evolutional Representation Learning Network (HERLN), which learns structural information and evolutional patterns of a TKG simultaneously, considering the characteristics of real-world networks: community structure, scale-free and temporal decaying. First, we find communities in the input TKG to make the encoding get more similar intra-community embeddings. Second, we design a Hawkes process-based relational graph convolutional network to cope with the event impact-decaying phenomenon. Third, we design a conditional decoding method to alleviate biases towards frequent entities caused by long-tailed distribution. Experimental results show that HERLN achieves significant improvements over the state-of-the-art models.