June 24 (Reuters) - Doximity Inc was valued at over $7 bln at start of trading on the New York Stock Exchange on Thursday, as shares of the social network for doctors opened more than 58% above their offer price. The company’s stock opened at $41.17 per share, up from the initial public offering (IPO) price of $26 per share. Reporting by Niket Nishant in Bengaluru; Editing by Vinay Dwivedi Our Standards: The Thomson Reuters Trust Principles.