Dynamic Network Evolution and Triadic Closure

Modeling evolving social networks, from triadic closure to block-structured communities.

Problem

How do local rules — like the tendency of a friend's friend to become a friend — shape the global structure of an evolving network?

Method

Built a stochastic dynamical system for triadic closure, analyzed quasi-stable states with mean-field theory, then extended the model to networks with block structure (e.g., two distinct communities) and added community detection plus maximum likelihood estimation.

Demonstrates

Mathematical abstraction, mean-field reasoning, and a practical pipeline from model design to estimation on social network data.

This project models how networks evolve when connections form preferentially between friends-of-friends.

For single-community networks, mean-field theory makes quasi-stable states computable and accurately predicts simulated dynamics. The model is then extended to multi-community settings — for example, friendships between two schools — where the analysis becomes more delicate but remains tractable.

A second contribution is a fitting procedure for real data: community detection and maximum likelihood estimation are derived from the triadic closure mechanism and a Markov model, allowing the framework to be applied to observed social network data with good agreement.