Patterns of Influence in a Recommendation Network

Abstract

Abstract. Information cascades are phenomena in which individuals adopt a new action or idea due to influence by others. As such a process spreads through an underlying social network, it can result in widespread adoption overall. We consider information cascades in the context of recommendations, and in particular study the patterns of cascading recommendations that arise in large social networks. We investigate a large person-to-person recommendation network, consisting of four million people who made sixteen million recommendations on half a million products. Such a dataset allows us to pose a number of fundamental questions: What kinds of cascades arise frequently in real life? What features distinguish them? We enumerate and count cascade subgraphs on large directed graphs; as one component of this, we develop a novel efficient heuristic based on graph isomorphism testing that scales to large datasets. We discover novel patterns: the distribution of cascade sizes is approximately heavy-tailed; cascades tend to be shallow, but occasional large bursts of propagation can occur. The relative abundance of different cascade subgraphs suggests subtle properties of the underlying social network and recommendation process.

The structure of online diffusion networks

“…As we discuss later, the results of these studies are consistent with ours; however, they have not directly addressed the central question of how much total adoption derives from viral spreading versus some other process. Of particular relevance is Leskovec et al [2006Leskovec et al [ , 2007, who analyzed product recommendations in a network of users of an e-commerce website with the primary objective of enumerating and counting the types of diffusion cascades that arose. As we do, they find that most cascades are small; however, they do not consider the subsequent-and from our perspective key-question of how much adoption is accounted for by the minority of large cascades.…”

“…In addition to this different objective, we note that Leskovec et al [2006Leskovec et al [ , 2007 investigate one domain with a high barrier to adoption: users must receive a recommendation and purchase a product to be counted as adopters. In contrast, we compare seven domains in which the type and the cost of adoption ranges greatly, from "retweeting" on Twitter to sending an email to purchasing.…”

“…In contrast, we compare seven domains in which the type and the cost of adoption ranges greatly, from "retweeting" on Twitter to sending an email to purchasing. Furthermore, our analysis covers domains in which there is ambiguity as to which is the parent node in the cascade (as in the recommendations domain of Leskovec et al [2006Leskovec et al [ , 2007) but also domains in which parents are uniquely identified through tracking URLs. The larger point is that because each prior study of online diffusion focused on a single web platform, such as Facebook [Sun et al 2009], Twitter [Bakshy et al 2011], Second Life [Bakshy et al 2009], or blog networks [Adar and Adamic 2005] and also invoked different metrics, it has previously been difficult to draw conclusions about online diffusion processes in general.…”

“…Accordingly, theoretical models of diffusion have generally imitated disease models in the sense that popular products are assumed to diffuse multiple steps from their origin in the manner of epidemics, "infecting" large numbers of people in the process [Watts 2002;Leskovec et al 2006]. Although this assumption is entirely plausible, empirical diffusion research has historically relied on aggregate data, such as cumulative adoption curves [Coleman et al 1957;Bass 1969;Young 2009;Iyengar et al 2010], which reveal only the total number of adopters at any given time.…”

“…In recent years, the increased availability of online social interaction data has offered new opportunities to map out the network structure of diffusion processes [Adar and Adamic 2005;Leskovec et al 2006Leskovec et al , 2007Bakshy et al 2009;Sun et al 2009;Bakshy et al 2011]. Here we leverage online diffusion data to address the question of how much total adoption derives from viral spreading versus some other process, as well as the implications of this empirical result for theoretical models of diffusion, in particular online diffusion.…”