IMDB network revisited: unveiling fractal and modular properties from a typical small-world network

TL;DR

This paper analyzes a subset of the IMDB movie collaboration network, revealing how link strength thresholds influence the network's fractal and modular properties, and demonstrating the network's self-similar structure through renormalization group analysis.

Contribution

It shows that imposing link strength thresholds transforms the network from small-world to fractal, and applies renormalization group analysis to characterize its self-similarity.

Findings

Network becomes small-world without thresholds.

Thresholds induce fractal structure.

Renormalization group analysis reveals self-similarity.

Abstract

We study a subset of the movie collaboration network, imdb.com, where only adult movies are included. We show that there are many benefits in using such a network, which can serve as a prototype for studying social interactions. We find that the strength of links, i.e., how many times two actors have collaborated with each other, is an important factor that can significantly influence the network topology. We see that when we link all actors in the same movie with each other, the network becomes small-world, lacking a proper modular structure. On the other hand, by imposing a threshold on the minimum number of links two actors should have to be in our studied subset, the network topology becomes naturally fractal. This occurs due to a large number of meaningless links, namely, links connecting actors that did not actually interact. We focus our analysis on the fractal and modular properties of this resulting network, and show that the renormalization group analysis can characterize the self-similar structure of these networks.