Visibility graph analysis of the grains and oilseeds indices

The Grains and Oilseeds Index (GOI) and its sub-indices of wheat, maize, soyabeans, rice, and barley are daily price indexes reflect the price changes of the global spot markets of staple agro-food crops. In this paper, we carry out a visibility graph (VG) analysis of the GOI and its five sub-indices. Our findings reveal that the degree distributions of the VGs, except for rice, exhibit exponentially truncated power-law tails, while the rice VG conforms to a power-law tail. The average clustering coefficients of the six VGs are quite large ($>0.5$) and exhibit a nice power-law relation with respect to the average degrees of the VGs. For each VG, the clustering coefficients of nodes are inversely proportional to their degrees for large degrees and are correlated to their degrees as a power law for small degrees. All the six VGs exhibit small-world characteristics. The degree-degree correlation coefficients shows that the VGs for maize and soyabeans indices exhibit weak assortative mixing patterns, while the other four VGs are weakly disassortative. The average nearest neighbor degree functions have similar patterns, and each function shows a more complex mixing pattern which decreases for small degrees, increases for mediate degrees, and decreases again for large degrees.