Failure in Complex Social Networks

Abstract

A class of inhomogenously wired networks called “scale-free” networks have been shown to be more robust against failure than more homogenously connected exponential networks. The robustness of scale-free networks consists in their ability to remain connected even when failure occurs. The diffusion of information and disease across a network only requires a single contact between nodes, making network connectivity the crucial determinant of whether or not these “simple contagions” will spread. However, for “complex contagions,” such as social movements, collective behaviors, and cultural and social norms, multiple reinforcing ties are needed to support the spread of a behavior diffusion. I show that scale-free networks are much less robust than exponential networks for the spread of complex contagions, which highlights the value of more homogenously distributed social networks for the robust transmission of collective behavior.

Keywords:

• collective dynamics
• complex contagions
• diffusion
• network robustness
• scale-free networks
• social dynamics
• social networks

Acknowledgments

I would like to thank the Robert Wood Johnson Foundation for support, and Nicholas Christakis and Albert-Laszlo Barabasi for useful comments and suggestions.

Notes

¹Asynchronous updating with random order and without replacement eliminates potential order effects and guarantees that every node is updated within a round of decision-making, which is defined as N time-steps.