Modeling Blog Dynamics Speaker: Michaela Götz Joint work with: Jure Leskovec, Mary McGlohon, Christos Faloutsos Cornell University Carnegie Mellon University Stanford University

Modeling the Blogosphere Blogosphere  System of interactions: ▫Entities: Bloggers, Posts, Topics, … ▫Relations:  Blogger publishes post  Post is about a topic  Post links to post Model  Simple set of rules (followed by a blogger) that creates these interactions Evaluation  Creating a synthetic blogosphere and comparing it to real blogosphere Motivation  Forecasting, advertising Michaela GötzModeling Blog DynamicsICWSM 2009

How is this different from modeling social networks? ▫2 networks combined: Blog vs. Post network B1 B4 B3 B2 B6 B7 B5 Blogosphere B1 B4 B3 B2 B6 B7 B Postnetwork Blognetwork Cascade Michaela GötzModeling Blog DynamicsICWSM 2009

▫2 networks combined: Blog vs. Post network ▫Complex temporal dynamics B4 B3 B2 B6 B7 B5 B1 How is this different from modeling social networks? Michaela GötzModeling Blog DynamicsICWSM 2009

▫2 networks combined: Blog vs. Post network ▫Complex temporal dynamics B1 B4 B3 B2 B6 B7 B5 B8 How is this different from modeling social networks? Our goal: Model micro-level interactions to create the macro-level patterns (both the temporal and topological) of the blogosphere Michaela GötzModeling Blog DynamicsICWSM 2009

Models – Related Work Michaela GötzModeling Blog DynamicsICWSM 2009 Realistic Topological PatternsRealistic Dynamical Patterns Links (SVM) [Adar and Adamic] Blog Mortality [Venolia] Links (Epidemiological Model) [Gruhl et al.] Links (Epidemiological Model) [Leskovec et al.] Inter-arrival time of s (Markov Chain) [Kleinberg] Links (Preferential Attachment) [Karandikar et al.] Time between answering two consecutive s (PA) [Barabasi; Vazquez] Blog

What are the properties of the blogosphere? Topological properties ▫Blog network ▫Post network Temporal properties ▫User posting activity ▫Popularity of posts over time (link creation) Michaela GötzModeling Blog DynamicsICWSM 2009

Some Topological Patterns Michaela GötzModeling Blog DynamicsICWSM 2009 Power law: [Leskovec et al.] Blog In-Degree Post In-Degree Cascade Size

Michaela GötzModeling Blog DynamicsICWSM 2009 Burstiness & Self-Similarity: Measure: Entropy at various resolutions Plot: Burstiness & Self-Similarity: Measure: Entropy at various resolutions Plot: Self-Similarity -> Linearity Burstiness -> Slope < 1 Self-Similarity -> Linearity Burstiness -> Slope < 1 Blogosphere – Some Temporal Patterns Time vs. Count Example 1 Aggregation Level vs. Entropy Example 2

Blogosphere – Some Temporal Patterns Michaela GötzModeling Blog DynamicsICWSM 2009 [McGlohon et al.] Inter-Posting Time Popularity: time t vs. #in-links received t days after publishing Burstiness of Posting Activity Burstiness & Self-Similarity: Measure: Entropy at various resolutions Plot: Burstiness & Self-Similarity: Measure: Entropy at various resolutions Plot:

Blogosphere - Dynamics B1 B4 B3 B2 B6 B7 B5 Michaela GötzModeling Blog DynamicsICWSM 2009 B8 WANTED: Model - Simple (no parameters) - Intuitive (local rules) - Creating Realistic Topology and Dynamics WANTED: Model - Simple (no parameters) - Intuitive (local rules) - Creating Realistic Topology and Dynamics

First try solution Let’s assume: ▫ Inter-posting times are sampled from exponential distribution ▫Links are created using Preferential Attachment But it won’t work: Inter-Posting Time Burstiness of Posting Activity Blog In-Degree Michaela GötzModeling Blog DynamicsICWSM 2009

Michaela GötzModeling Blog DynamicsICWSM 2009 Our Model ZC In Every Round For Every Blog In Every Round For Every Blog post P no link create link choose neighbor B choose neighbor B choose non-neighbor B choose non-neighbor B choose post Q of B choose post Q of B link to random posts upward in the cascade link to random posts upward in the cascade “random walk” …… “explore”“exploit” “link expansion” /2

Michaela GötzModeling Blog DynamicsICWSM 2009 Our Model ZC In Every Round For Every Blog In Every Round For Every Blog post P no link create link choose neighbor B choose neighbor B choose non-neighbor B choose non-neighbor B choose post Q of B choose post Q of B link to random posts upward in the cascade link to random posts upward in the cascade “random walk” …… “explore”“exploit” “link expansion” /2 B3 B2 B

Michaela GötzModeling Blog DynamicsICWSM 2009 Our Model ZC In Every Round For Every Blog In Every Round For Every Blog post P no link create link choose neighbor B choose neighbor B choose non-neighbor B choose non-neighbor B choose post Q of B choose post Q of B link to random posts upward in the cascade link to random posts upward in the cascade “random walk” …… “explore”“exploit” “link expansion” /2 B3 B2 B

Michaela GötzModeling Blog DynamicsICWSM 2009 Our Model ZC In Every Round For Every Blog In Every Round For Every Blog post P no link create link choose neighbor B choose neighbor B choose non-neighbor B choose non-neighbor B choose post Q of B choose post Q of B link to random posts upward in the cascade link to random posts upward in the cascade “random walk” …… “explore”“exploit” “link expansion” /2 B3 B2 B ?

Michaela GötzModeling Blog DynamicsICWSM 2009 Our Model ZC In Every Round For Every Blog In Every Round For Every Blog post P no link create link choose neighbor B choose neighbor B choose non-neighbor B choose non-neighbor B choose post Q of B choose post Q of B link to random posts upward in the cascade link to random posts upward in the cascade “random walk” …… “explore”“exploit” “link expansion” /2 B3 B2 B

Michaela GötzModeling Blog DynamicsICWSM 2009 Our Model ZC In Every Round For Every Blog In Every Round For Every Blog post P no link create link choose neighbor B choose neighbor B choose non-neighbor B choose non-neighbor B choose post Q of B choose post Q of B link to random posts upward in the cascade link to random posts upward in the cascade “random walk” …… “explore”“exploit” “link expansion” /2 B3 B2 B

Michaela GötzModeling Blog DynamicsICWSM 2009 Our Model ZC In Every Round For Every Blog In Every Round For Every Blog post P no link create link choose neighbor B choose neighbor B choose non-neighbor B choose non-neighbor B choose post Q of B choose post Q of B link to random posts upward in the cascade link to random posts upward in the cascade “random walk” …… “explore”“exploit” “link expansion” /2 B3 B2 B

Michaela GötzModeling Blog DynamicsICWSM 2009 post P no link create link choose neighbor B choose neighbor B choose non-neighbor B choose non-neighbor B choose post Q of B choose post Q of B link to random posts upward in the cascade link to random posts upward in the cascade “random walk” …… “explore”“exploit” “link expansion” /2 Our Model ZC Properties - Simple (no parameters) - Intuitive (local rules) Properties - Simple (no parameters) - Intuitive (local rules) Theorem: The interposting time of ZC follows a power- law with exponent -1.5 Theorem: The interposting time of ZC follows a power- law with exponent -1.5 Theorem: The posting activity is self-similar and bursty.

Michaela GötzModeling Blog DynamicsICWSM 2009 Our Model ZC – Experimental Evaluation Inter-Posting TimeBurstiness of Posting Activity Real Data Simulation Popularity over time 45k blogs, 2.2 million posts [Glance et al.] 45k blogs, 2.2 million posts

Michaela GötzModeling Blog DynamicsICWSM 2009 Post In-Degree Cascade Size Our Model ZC – Experimental Evaluation Blog In-Degree Real Data Simulation

Michaela GötzModeling Blog DynamicsICWSM 2009 Conclusions Model ZC of the Blogosphere - Simple (no parameters) - Intuitive (local rules) - Creating Realistic Blogosphere: - evaluated on 3 topological patterns - evaluated on 3 temporal patterns - Useful for forecasting and to explore dynamics for advertising Model ZC of the Blogosphere - Simple (no parameters) - Intuitive (local rules) - Creating Realistic Blogosphere: - evaluated on 3 topological patterns - evaluated on 3 temporal patterns - Useful for forecasting and to explore dynamics for advertising post P no link create link choose neighbor B choose neighbor B choose non-neighbor B choose non-neighbor B choose post Q of B choose post Q of B link to random posts upward in the cascade link to random posts upward in the cascade “random walk” …… “explore”“exploit” “link expansion” /2

Michaela GötzModeling Blog DynamicsICWSM 2009 Thanks! post P no link create link choose neighbor B choose neighbor B choose non-neighbor B choose non-neighbor B choose post Q of B choose post Q of B link to random posts upward in the cascade link to random posts upward in the cascade “random walk” …… “explore”“exploit” “link expansion” /2