The notion of genre has been widely explored using quantitative methods from both lexical and syntactical perspectives. However, discourse structure has rarely been used to examine genre. Mostly concerned with the interrelation of discourse units, discourse structure can play a crucial role in genre analysis. Nevertheless, few quantitative studies have explored genre distinctions from a discourse structure perspective. Here, we use two English discourse corpora (RST-DT and GUM) to investigate discourse structure from a novel viewpoint. The RST-DT is divided into four small subcorpora distinguished according to genre, and another corpus (GUM) containing seven genres are used for cross-verification. An RST (rhetorical structure theory) tree is converted into dependency representations by taking information from RST annotations to calculate the discourse distance through a process similar to that used to calculate syntactic dependency distance. Moreover, the data on dependency representations deriving from the two corpora are readily convertible into network data. Afterwards, we examine different genres in the two corpora by combining discourse distance and discourse network. The two methods are mutually complementary in comprehensively revealing the distinctiveness of various genres. Accordingly, we propose an effective quantitative method for assessing genre differences using discourse distance and discourse network. This quantitative study can help us better understand the nature of genre.