Network Complexity and Financial Behavior – Volume Distribution over Price in Financial Market

A complex system consists of a lot of interactive individuals, agents, or units. It occurs widely but is hard to model in both natural and social sciences. Its behavior is neither regular nor random. However, it has some kinds of structures which capture our interesting to study. We can apply network theories to analyze the behaviors of a complex system which we can find almost everywhere in physics, chemistry, bioscience, psychology, sociology, organization structure, urban traffic, and economics and finance etc. After a brief perspective on the historical development and applications from networks to complex networks, this review converges to the application in finance. We do so, partly because there are abundant trading big data every day available for the empirical tests that have already rejected basic assumptions in neoclassical finance over the past 40 years, and partly because market participants or agents are interacted themselves with one another and have been adequately studied in empirical tests. Today, we have already come at a turning point in behavioral and social finance since its empirical revolution, from which someone is destined to propose a unified theory in the history of economic sciences. The theory based on a price-volume probability wave differential equation views stock market as the complex networks that lie between price random walks and long-term predictable price dynamic equilibriums in terms of its fundamentals. There are many ‘small-world’ market dynamic equilibriums, which are displayed by intraday cumulative trading volume distributions over a price range (nodes) and connected by the nonlinear jump return of a price equilibrium point (edges). Following this direction, we attempt to further develop a theory for complex networks, control systems, systems sciences, and cognitive intelligent sciences. It helps us understand an interactive society, suggesting policy guidance on quarantine and mask wearing against COVID-19 pandemic