Identifying structure underlying high-dimensional data is a common challenge across scientific disciplines. We revisit correspondence analysis (CA), a classical method revealing such structures, from a network perspective. We present the poorly-known equivalence of CA to spectral clustering and graph-embedding techniques. We point out a number of complementary interpretations of CA results, other than its traditional interpretation as an ordination technique. These interpretations relate to the structure of the underlying networks. We then discuss an empirical example drawn from ecology, where we apply CA to the global distribution of Carnivora species to show how both the clustering and ordination interpretation can be used to find gradients in clustered data. In the second empirical example, we revisit the economic complexity index as an application of correspondence analysis, and use the different interpretations of the method to shed new light on the empirical results within this literature.