Before revision:  We present a general approach describing the financial network by a random graph , where we distinguish vertices (institutions) of different types - for example core/periphery - and let edge probabilities and weights (exposures ) depend on the types of both  the receiving and the sending vertex  .
After revision:  We present a general approach describing the financial network by a random graph , where we distinguish vertices (institutions) of different types - for example core/periphery - and let edge probabilities and weights (exposures ) depend on the types of both the receiving and the sending vertex plus additional parameters .