Topological measures for identifying and predicting the spread of complex contagions

Topological measures for identifying and predicting the spread of complex contagions. Douglas Guilbeault & Damon Centola. Nature Communications volume 12, Article number: 4430. Jul 20 2021. https://www.nature.com/articles/s41467-021-24704-6

Abstract: The standard measure of distance in social networks – average shortest path length – assumes a model of “simple” contagion, in which people only need exposure to influence from one peer to adopt the contagion. However, many social phenomena are “complex” contagions, for which people need exposure to multiple peers before they adopt. Here, we show that the classical measure of path length fails to define network connectedness and node centrality for complex contagions. Centrality measures and seeding strategies based on the classical definition of path length frequently misidentify the network features that are most effective for spreading complex contagions. To address these issues, we derive measures of complex path length and complex centrality, which significantly improve the capacity to identify the network structures and central individuals best suited for spreading complex contagions. We validate our theory using empirical data on the spread of a microfinance program in 43 rural Indian villages.

Discussion

Path length is one of the most important and influential measures of network structure. It underlies nearly every theory of social connectedness, social distance, and social influence within social networks. Here we show that the classical measure of simple path length, upon which most popular measures of node centrality depend, implicitly assumes the spreading dynamics of simple contagion. This assumption has resulted in several puzzling empirical findings in which individuals with putatively low centrality have been shown to be more influential for diffusion than individuals with high centrality (according to prominent measures of degree centrality, betweenness centrality, eigenvector centrality, k-core centrality, and percolation centrality). We derive new topological definitions of bridge width, path length, and centrality, which provide general topological measures for accurately estimating the network properties of connectedness, distance, and centrality for the spread of complex social contagions. We find that these measures offer significant theoretical improvements over existing measures of population-level network topology, and individual-level node centrality, for predicting the network properties that will increase the spread of complex social contagions.

Our findings offer several noteworthy departures from the dominant strategies for applying network theory to problems of social diffusion1,3,5,29,42,43,44,45,46,47. First, a common assumption among both theoretical and applied studies of network diffusion is that people with more connections are more influential5,21,22,29,30,42,43,44,45. Our findings disagree with the frequently asserted claim in this literature that degree centrality is an effective, if approximate, means of identifying the most influential individuals within a social network, regardless of context5,21,22,29,30,42,43,44,45. Second, a common assumption within organizational studies of social networks is that information brokers—i.e., people who participate in multiple distinct network communities that are largely disconnected—have outsized influence because they are the gatekeepers in the flow of contagions between communities46,47. This assumption has resulted in betweenness centrality becoming one of the most widely used measures of network influence within organizational theory1,27,29,42,43,46,47,48,49. By contrast, our findings indicate that network locations with low degree centrality and low betweenness centrality may nevertheless be the most influential locations in the population. We also find that individuals with the highest levels of degree centrality and betweenness centrality typically occupy ineffective network positions for initiating the spread of complex social contagions—including health behaviors8,9, linguistic conventions6,12,13, political memes14, social movements15,16, and complementary technologies6,10. We anticipate that an important direction for future work will be the exploration of new algorithms for computing the theoretical properties of complex path length and complex centrality, which may benefit from recent developments that improve the scalability of novel algorithmic techniques50. Another interesting direction for future research is the application of our topological measures for identifying specific network locations that can be used to efficiently stop the spread of an existing complex contagion from one part of a network to the entire population (akin to the problem of network “immunization” for simple contagions)6,51,52.