A Random Walk Approach to Modeling the Dynamics of the Blogosphere

1. A Random Walk Approach to Modeling theDynamics of the Blogosphere Alex X. Liu Dept. of Computer Science and Engineering Michigan State University Joint work with M. ZubairShafiq

2. Background • Important niche of online social networks • Blogosphere consists of two networks • Blog network (Nodes = Blogs, Edges = Hyperlinks) • Post network (Node = Posts, Edges = Hyperlinks) Blog network Post network Blogosphere

3. Motivation • Modeling the evolution dynamics of blogosphere • How do blogs produce posts? • What are underlying mechanisms? • Applications • Advertising • Forecasting • Studying effect of probing for improving platform design

4. Problem Statement • Model • Generative model of individual bloggers in the blogosphere • Replicated for all bloggers • Allowed to execute over a given period of time • Requirements • Only use local mechanisms • Intuitive and realistic • Evaluation • Ground truth: properties of real-world blogosphere • Temporal properties, e.g. inter-posting time • Topological properties, e.g. degree distribution

5. Limitations of Prior Art • Only Topological properties • Second space [Karandikar08ICWSM] • Ad hoc in nature • Multiple input parameters • Kronecker graphs [Leskovec07ICML] • Not specifically designed for blogosphere • Only Temporal properties • Randomized blogspace [Kumar03WWW) • Mostly focuses on burstiness property • Both Topological and temporal properties • Zero-crossing [Gotz09ICWSM] • No parameters, cannot control properties • Uses global properties, e.g. total number of in-links to a blog

6. Proposed Approach • Random walk process • Different variants of the random walk process • Emulate the topological and temporal characteristics of individual bloggers Two dimensional One dimensional

7. Flow Chart of the Proposed Model • Series of random walks for each blogger • Random walk 1 • Post at zero-crossing • Random walk 2 • Select new blogs to link (explore) • Random walk 3 • Select previously linked blogs to link (exploit) • Random walk 4 • Select post to link • Random walk 5 • Link to posts referred by the selected post

8. Proposed Model • Random walk 1 (one dimensional random walk) • Temporal dynamics of a blogger's posting behavior • Publish a new post at zero crossing • Reproduce burstiness, self-similarity in publishing behavior • Slope of entropy plot ≈ 0.7 < 1

9. Proposed Model • Random walk 2 (random walk on blog graph) • Select new blogs to link (Explore) • Starts at a randomly chosen node of the blog graph • Blog reached at the end of random walk is selected • Random walk 3 (random walk on blog graph) • Select previously linked blogs to link (Exploit) • Starts at the corresponding node of the blog graph • Blog reached at the end of random walk is selected

10. Proposed Model • Random walk 4 (random walk on post graph) • To select a post from the selected blog • Ordered in the reverse-chronological order • Initiates at the latest post • Post reached at the end of random walk is selected • Random walk 5 (random walk on post graph) • Blogger recursively refers to some out-links of the selected post (link expansion) • Starts at the post selected in random walk 4 • Post reached at the end of random walk is selected

11. Inter-posting times • Definition: time between two consecutive posts • The distribution of inter-posting times follows power-law • Implication: blogging activity is characterized by long periods of inactivity separated by short periods of activity

12. Blog in-degree • Definition: count of in-linking blogs • The distribution of blog in-degree times follows power-law • Implication: only a few blogs receive large number of in-links and a majority of blogs remain unnoticed

13. Post in-degree • Definition: count of in-linking posts • The distribution of post in-degree times follows power-law • Implication: only a few posts receive large number of in-links and a majority of posts remain unnoticed

14. PageRank • Definition: PageRank or Eigenvector centrality assign importance weight assigned to every node in a network • The distribution of PageRank times follows power-law • Implication: only afew posts are highly cited

15. Future Work • Study affect of varying the length of random walk on structural properties of generated blogospheres • Structural properties: • Transitivity • Average clustering coefficient • Average shortest path length • Size of largest connected component

16. Conclusions • Propose random walk based model to simulate the evolution of blogosphere • Intuitive and simple • Simultaneously considers temporal and topological properties • Model works with the local information, does not utilize global information • Experiments show that the properties of evolved blogosphere follow those of real-world blogosphere • Structural properties can be controlled by varying the length of random walk

17. Questions?