In what ways are small-world and scale-free networks interrelated?

Abstract

Small-world networks are characterized by local clustering and shortcut ties that reduce the path-length between the clusters. Scale-free networks, on the other hand, take a skewed degree distribution. Few empirical works have aimed to interrelate or integrate these influential social theories, and here we address this issue. Our empirical context spans several winter sport destinations and we retrospectively reconstruct the development of an inter-firm network. When the path-length at the outset is large (short) the concept is negatively (positively) associated with the scale-free distribution. Other studies have shown that scale-free networks are vulnerable for targeted attacks, and an implication from our finding is that small-world networks can also be vulnerable for targeted attacks (particularly when the path-length's association with the scale-free distribution reaches a maximum). We also find an inverse relationship between local clustering and scale-free distribution, but the association may be spurious.