Figure 1: Example LinkedIn signup cascade
Many of the popular websites such as LinkedIn power their growth through guest invitations from existing members to non-members. New members joining can also send such guest invitations resulting in cascade of membership growth at a large scale. How does such cascade of membership growth looks like? How viral are these cascades?
Recently we analyzed LinkedIn’s growth through such guest invitations addressing these questions, the largest structural analysis of cascading growth diffusion, and published our work in the 24th International World Wide Web Conference (WWW) 2015:
LinkedIn is the largest professional network with more than 360 million members. LinkedIn membership has grown through warm signups because of guest invitations and direct signup at the site without an invitation. A significant fraction of the members joined LinkedIn through the cascading guest invitations resulting in warm signups. The cascading signups can be organized into a collection of trees: each time a member signs up directly, she becomes the root of a new tree, and every user who signs up by accepting an invitations from a member A becomes the child of member A in the tree with member A. One example of such a tree is shown (at the top) in Figure 1. We find that LinkedIn’s signup cascade trees are huge, very viral (compared to previously studied diffusion phenomenon), and members remain active for a long time in sending guest invitations resulting in more warm signups.
Figure 2: Pattern of LinkedIn’s cascade trees growth over time
How does LinkedIn’s cascade trees grow in size over time? In Figure 2 we plot the growth of the 1000 biggest cascade trees on LinkedIn. We see a surprisingly robust growth pattern in these cascade trees (and all the trees as well). Also, we observe that the number of cascade trees are growing over time at a deliberate pace. In short, we are observing persistent, parallel increase in the number of cascade trees and size contributing to warm signup growth at LinkedIn.
How does growth diffusion affects the characteristics of members present in the cascade trees? In addition to analyzing the structure of growth cascade trees, we also connect interaction between the characteristics of the members present in the trees and structure of the trees. We find the geography and industry play an important role in the cascade and shows similarity between the inviter and invitee. Figure 3 shows within cascade tree similarity and compares with between tree similarity for members present in the tree on country, region, industry, engagement, and seniority among growth cascade trees. We observe that similarity within tree on country and industry dimensions are much higher compared to between-tree similarities.
Figure 3: Within-tree and between-tree similarity (homophily) on country, region, industry, engagement, and seniority among growth cascade trees.
Surprisingly similarity between inviter and invitee is not sufficient to explain within tree similarity we observe. We find that higher order Markov models, in which a node’s characteristics not only depend on the parent but ancestors as well, produce a level of similarity and homophily that closely matches observed data as shown in Figure 4.
Figure 4: Root-guessing experiment where we are trying to predict the country of root node based on the country of a given node.
This is the largest growth diffusion study (that we are aware of) and for more details check out our paper:
Global Diffusion via Cascading Invitations: Structure, Growth, and Homophily, Ashton Anderson, Daniel Huttenlocker, Jon Kleinberg, Jure Leskovec, and Mitul Tiwari. In the Proceedings of the 24th International World Wide Web Conference (WWW), May 2015.