Statistical and Machine Learning Approaches for Network Analysis

2.14 Conclusion

In this chapter, we introduced several statistical properties of real-world networks, such as the scale-free property and small-world property, by comparing these networks to random networks. That is, the random network models (e.g., the ER model and configuration model) are powerful null models for network analysis. For example, we can find the network motif by comparing between real-world networks and random (null model) networks as explained in Section 2.8. Furthermore, network measures are not overestimated or underestimated by considering random network models because the models detect the bias against structural complexity.

The nonrandom structural patterns (especially scale-free property) are known to critically influence the dynamics of networks, such as epidemic spreading (e.g., [50]) and synchronization (e.g., [51]), implying the importance of network structure. Moreover, we discussed several network models and the reproduction of their structural properties. Since these models can control the tendency of structural patterns using a few parameters, they are useful to investigate the relationship between structural patterns and dynamics on networks.

The structural patterns and statistical laws help in the modeling of complex systems. For example, we may discuss the significance of unknown parameters, and simplify model representations. Furthermore, we find that network models can be used to predict missing information. The understanding of real-world networks ...