Link Graph and Data-Driven Graphs as Complex Networks: Comparative Study

The link and data-driven graphs corresponding to the same dataset are studied as complex networks. It appears that a link graph features the majority of complex networks characteristics, whereas the corresponding data-driven graphs feature only part of these characteristics. Some characteristics appear to be more stable, when one moves from a link graph to data-driven graphs and over data-driven graphs, than others. In particular, one observes giant components and power-law community size distributions for most link and data-driven graphs. Also, data-driven graphs usually retain small world property and relatively large values of clustering coefficients, provided the same holds true for the respective link graph. Meanwhile, only the ε-ball neighbourhood graph and the Gabriel graph exhibit power-law degree distributions as their link counterparts do. The assortativity coefficient is essentially corrupted when one moves from a link graph to data graphs. Sometimes, assortativity alters to disassortativity. Among all data-driven graphs considered, the Gabriel graph seems to retain most properties of complex networks.