Universal law in the crude oil market based on visibility graph algorithm and network structure

Price fluctuations in the crude oil market is important to both financial practitioners and market participants, since it not only affects investors' investment, portfolio allocation and risk evaluation, but also influences strategic planning and market decisions. By using visibility graph algorithm (VG), the time series of 32-year crude oil price is converted to a corresponding single spot and futures price network respectively. The network topological structure implies that the single spot and futures price network both follow the power-law distribution and power-law index gamma = 2.8. When the crude oil market suffers from financial shock, stable price market is broken and reaches a collapse critical state. And, we find that the biggest connection cluster of price network with two communities S(r, p(c)) has a scaling relationship with interconnected nodes fraction r, and the scale index is delta = 1.3 near the critical point for different shock scenarios. Besides, similar to the results in a single price network, the rate of change of S(r, p(c)) also shows a scaling relationship with p - p(c) (the difference between attack strength 1 - p and critical attack strength p(c)), the scale index gamma = 1.5. Particularly, these two indices gamma and delta satisfy the universal Wisdom's law. According to the above relationship, one can observe the changes of the biggest connection cluster of price network near critical attack strength, and make adjustments of investment quickly to avoid huge losses by comprehending this laws.