Diffusion of complex contagions is shaped by a trade-off between reach and reinforcement

How does social network structure amplify or stifle behavior diffusion? Existing theory suggests that when social reinforcement makes the adoption of behavior more likely, it should spread more-both farther and faster-on clustered networks with redundant ties. Conversely, if adoption does not benefit from social reinforcement, it should spread more on random networks which avoid such redundancies. We develop a model of behavior diffusion with tunable probabilistic adoption and social reinforcement parameters to systematically evaluate the conditions under which clustered networks spread behavior better than random networks. Using simulations and analytical methods, we identify precise boundaries in the parameter space where one network type outperforms the other or they perform equally. We find that, in most cases, random networks spread behavior as far or farther than clustered networks, even when social reinforcement increases adoption. Although we find that probabilistic, socially reinforced behaviors can spread farther on clustered networks in some cases, this is not the dominant pattern. Clustered networks are even less advantageous when individuals remain influential for longer after adopting, have more neighbors, or need more neighbors before social reinforcement takes effect. Under such conditions, clustering tends to help only when adoption is nearly deterministic, which is not representative of socially reinforced behaviors more generally. Clustered networks outperform random networks by a 5% margin in only 22% of the parameter space under its most favorable conditions. This pattern reflects a fundamental trade-off: Random ties enhance reach, while clustered ties enhance social reinforcement.