Abstract: The wide application of social network and Internet finance brings opportunities and challenges to the development of the financial market. For example, Alipay is widely used for payment online and offline in China, and Lending Club is used in American as a P2P platform. The financial market is more complex and diverse than ever. Traditional financial markets and regulation theories are hard to adapt to the development of the financial market and risk management needs. What is the new equilibrium of the financial market which integrates social network and Internet finance? How do the social network and social relationship affect financial market? What is the role of Internet finance in the financial market? These are some new problems worth studying.
In this paper, considering the complex networks relationships brought by social network and Internet finance, an integrated capital flow network and social network financial market supernetwork model is built to show the complex relationships among financial market participants, and variational inequalities method is used to study the equilibrium of the financial market.
First,the credit punishment function and operational risk function that considered Intenet finance are given. And taking into account the strengthening of social network relations can improve the transparency of information, reduce transaction costs and risks, a four-layer supernetwork model which is composed by social network and capital flow network is established. The four layer are capital supplier layer, Internet financial layer, traditional financial layer, capital demander layer respectively. Then,an analysis of the behavior of the participants in the proposed supernetwork model is performed is performed, the multi-objective decision model that includs the maximum net income, the social network relationship between maximization and risk minimization goals si gotten. Next, using variational inequality theory, the financial market equilibrium conditions are studied. Finally, an example for simulating is given to test the validity of the model, and the management insight for Internet financial intermediaries and traditional financial intermediaries is discussed.
The results show that when considering social network relationships, the financial market equilibrium is different. There are some effects on Internet financial intermediaries and traditional financial intermediaries. That is to say, as the development of social network and Internet finance, strengthening the cooperation and collaboration between Internet financial intermediaries and traditional financial intermediaries is of great significance to enhance the stability and effectiveness of the financial market and reduce the financial risk.
The paper's result is useful for financial regulation department, Internet finance and traditional financial intermediaries.

Key words: equilibrium, Internet finance, social network,supernetwork, variational inequality