An Efficient Bipartite Graph Sampling Algorithm with Prescribed Degree Sequences

The structure of financial networks plays a crucial role in managing financial risks, particularly in the assessment of systemic risk. However, the true structure of these networks is often difficult to observe directly. This makes it essential to develop methods for sampling possible network configurations based on partial information, such as node degree sequences. In this paper, we consider the problem of sampling bipartite graphs (e.g., bank-asset networks) under such partial information. We first derive exact bounds on the number of nodes that can be connected at each step, given a prescribed degree sequence. Building on these bounds, we then introduce a weighted-balanced random sampling algorithm for generating bipartite graphs that are consistent with the observed degrees, and illustrate how the algorithm works through an example. In addition, we demonstrate the effectiveness of the proposed algorithm through numerical experiments.