Eating disorders are complex mental disorders and responsible for the highest mortality rate among mental illnesses. Recent studies reveal that user-generated content on social media provides useful information in understanding these disorders. Most previous studies focus on studying communities of people who discuss eating disorders on social media, while few studies have explored community structures and interactions among individuals who suffer from this disease over social media. In this paper, we first develop a snowball sampling method to automatically gather individuals who self-identify as eating disordered in their profile descriptions, as well as their social network connections with one another on Twitter. Then, we verify the effectiveness of our sampling method by: 1. quantifying differences between the sampled eating disordered users and two sets of reference data collected for non-disordered users in social status, behavioral patterns and psychometric properties; 2. building predictive models to classify eating disordered and non-disordered users. Finally, leveraging the data of social connections between eating disordered individuals on Twitter, we present the first homophily study among eating-disorder communities on social media. Our findings shed new light on how an eating-disorder community develops on social media.