Today, many users are actively using Twitter to express their opinions and to share information. Thanks to the availability of the data, researchers have studied behaviours and social networks of these users. International migration studies have also benefited from this social media platform to improve migration statistics. Although diverse types of social networks have been studied so far on Twitter, social networks of migrants and natives have not been studied before. This paper aims to fill this gap by studying characteristics and behaviours of migrants and natives on Twitter. To do so, we perform a general assessment of features including profiles and tweets, and an extensive network analysis on the network.