In a crowdsourcing contest, a requester holding a task posts it to a crowd. People in the crowd then compete with each other to win the rewards. Although in real life, a crowd is usually networked and people influence each other via social ties, existing crowdsourcing contest theories do not aim to answer how interpersonal relationships influence peoples' incentives and behaviors, and thereby affect the crowdsourcing performance. In this work, we novelly take peoples' social ties as a key factor in the modeling and designing of agents' incentives for crowdsourcing contests. We then establish a new contest mechanism by which the requester can impel agents to invite their neighbours to contribute to the task. The mechanism has a simple rule and is very easy for agents to play. According to our equilibrium analysis, in the Bayesian Nash equilibrium agents' behaviors show a vast diversity, capturing that besides the intrinsic ability, the social ties among agents also play a central role for decision-making. After that, we design an effective algorithm to automatically compute the Bayesian Nash equilibrium of the invitation crowdsourcing contest and further adapt it to large graphs. Both theoretical and empirical results show that, the invitation crowdsourcing contest can substantially enlarge the number of contributors, whereby the requester can obtain significantly better solutions without a large advertisement expenditure.