Social networks have garnered much attention recently. Several studies have been undertaken to extract social networks among people, companies, and so on automatically from the web. For use in social sciences, social networks enable analyses of the performance and valuation of companies. This paper describes an attempt to learn ranking of companies from a social network that has been mined from the web. For example, if we seek to rank companies by market value, we can extract the social network of the company from the web and discern and subsequently learn a ranking model based on the social network. Consequently, we can predict the ranking of a new company by mining its relations to other companies. Using our approach, we first extract relational data of different kinds from the web. We then construct social networks using several relevance measures in addition to text analysis. Subsequently, the relations are integrated to maximize the ranking predictability. We also integrate several relations into a combined-relational network and use the latest ranking learning algorithm to obtain the ranking model. Additionally, we propose the use of centrality scores of companies on the network as features for ranking. We conducted an experiment using the social network among 312 Japanese companies related to the electrical products industry to learn and predict the ranking of companies according to their market capitalization. This study specifically examines a new approach to using web information for advanced analysis by integrating multiple relations among named entities.