SOC and Complex Networks

Abstract

The main thread of this chapter is the power law distribution, which is the most common mathematical description of SOC. We first introduce some important concepts related to SOC, such as the scale-free distribution, fluctuation and long-range correlation. We then discuss the mathematical description of the mechanism of phase transitions and extreme events in complex systems. We also review some key definitions in complex networks, such as the node degree distribution, average path length, clustering coefficient and betweenness centrality. Special attention is paid to the small-world networks and scale-free networks, which are the most popular models used for complex networks. Finally, topics of community structures, central node identification, structural vulnerability and network synchronization are covered in order to investigate the relationship between a network’s topology and its functionalities.