Malik Magdon-Ismail, Konstantin Mertsalov, Mark Goldberg Models of Communication Dynamics for Simulation of Information Diffusion Malik Magdon-Ismail, Konstantin Mertsalov, Mark Goldberg

Motivation Important to understand information diffusion in social networks Viral marketing, gossip, rumors, etc. Social Networks are dynamic Edges and nodes change with time. Cannot repeat historical dynamics, so need to simulate dynamics for research.

LiveJournal Data Construct sequence of comment graphs (every week) Alice’s Blog Bill’s Blog Alice Posted Bill Posted A Bill commented Alice commented Cory commented Edges: (A,B); (C,B) (D,B) Edges: (B,A); (C,A) Alice commented Cory commented Dave commented D B C Construct sequence of comment graphs (every week) 3

Dynamics of LiveJournal Network 60 weeks Per week: 153,028 nodes 510,317 edges Very dynamic: 70% of edges change from week to week 4

Diffusion in Dynamic Networks Time: T Time: T+1 Time: T+2 A B F E H C D G J A B F E H C D G J A B F E H C D G J Static C A B F E H C D G J A B F E H C D G J A B D Dynamic F E J H G

Diffusion in LiveJournal Blogs Linear Threshold Independent Cascade Diffusion model and network dynamics have a big impact on infection.

Goal Can we model the network dynamics so that diffusion in the model mimics diffusion in the real network?

Network at iteration t+1 Modeling Dynamics Input Network at iteration t Output Network at iteration t+1 C C A A B D B D E J E J F F H H G G

Step 2: Local Attachment A General Model Input: Gt Step 1: Find Locality C A C B A D B D F E J F E J H G H G Step 2: Local Attachment Output: Gt+1 C A B C D A B D F E J F E J H G H G

Ingredients to General Model 1. What is the locality of the node ? C A Global: all nodes k-Neighborhood Community* B D Gt F E J H G 2. How to attach within locality ? C A B Uniform Preferential Attachment Random walk D Gt+1 F E J H G * Community = union of overlapping clusters [Baumes, Goldberg, Magdon-Ismail 2005]

Diffusion Models Linear Threshold: C C Linear Threshold: Node i has a susceptibility fraction T(i). Node i infected if at least T(i) neighbors are infected. A A B B D D F F E J E J H H G G C C A A Independent Cascade: Every edge (i,j) has transmission prob. P(i,j). Nodes have one chance to infect neighbors. B B D D 0.3 0.2 F F E J E J 0.4 H H G G

Diffusion in Dynamic Network Diffusion Model Network Dynamics Cascade Real LiveJournal Diffusion Progression Locality and Attachment Threshold Model

Static Aggregated Network Results Dynamic Network Static Aggregated Network Cascade Threshold

Conclusions Dynamics of the network strongly affects it’s diffusion properties Global random link dynamics does not model dynamics correctly Social network links evolve through locality (social groups), eg. cluster-based communities+PA produces diffusion faithful network dynamics.

Thank you !