Simple Paths and Cycles of Directed Graph for Stock Trading Network Based on STP

The stock trading relationship of buyers and sellers in the stock market can be characterized by a directed graph. It is an important way to study stock trading network through simple directed paths and cycles. In the present paper, we establish a seeking model of simple directed paths and cycles, and obtain some necessary and sufficient conditions for simple directed path and cycle in the directed graph. The algorithms of finding simple directed path and cycle of any specified length are given. The main approach we used is the semi-tensor product of matrices, which can reduce the search space. An illustrative example is given to show that the theoretical results and algorithms are effective.