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. 2013 Jun 24;8(6):e66443.
doi: 10.1371/journal.pone.0066443. Print 2013.

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

Lazaros K Gallos  1 , Fabricio Q Potiguar, José S Andrade Jr, Hernan A Makse
Affiliations

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

Lazaros K Gallos et al. PLoS One. .

Erratum in

  • PLoS One. 2013;8(8). doi:10.1371/annotation/7ce29312-158e-49b2-b530-6aca07751cea

Abstract

We study a subset of the movie collaboration network, http://www.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.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Number of actors per year and number of movies per year for the entire IMDB database (lines) and for the adult IMDB database (symbols).
In the plot the adult IMDB points have been multiplied by a factor of 5 for clarity. Inset: the same numbers on a logarithmic y-scale.
Figure 2
Figure 2. Comparison of the IMDB network to the adult IMDB network.
a) Probability distribution that a number formula image of actors participated in a movie (as reported in IMDB). b) Distribution of the links weights, or equivalently, the probability that two actors have participated in formula image movies together.
Figure 3
Figure 3. Snapshots of the ‘adult IMDB’ network, where two actors are connected if they have co-starred in at least a) , b) , c) , or d) movies, respectively.
Only the largest connected component is shown, and the corresponding network sizes are formula image, 14444, 5315, and 2100 actors, respectively.
Figure 4
Figure 4. Degree distribution of the adult IMDB network, for different connection strengths, , 2, 4, or 8 movies, respectively.
The solid line has a slope, the exponent of the power law degree distribution, formula image (see text).
Figure 5
Figure 5. Probability distribution of the shortest paths in networks with varying weight threshold .
Inset: Maximum diameter in the network as a function of formula image.
Figure 6
Figure 6. Scaling of the number of boxes as a function of the maximum box diameter , for the adult IMDB network and for different values.
Except for formula image, the other networks have a fractal dimension, shown by the dashed line with slope, formula image.
Figure 7
Figure 7. Scaling of the modularity as a function of the maximum box diameter , for the adult IMDB network and for different values.
All networks scale with formula image, with a slope close to formula image, as shown by the dashed line with the same slope value.
Figure 8
Figure 8. Networks resulting from the box-covering procedure at different values.
Top row: Adult IMDB network at formula image. Bottom row: Adult IMDB network at formula image.
Figure 9
Figure 9. Variation of the average degree in the IMDB network for different values, as a function of the average box mass .
See this image and copyright information in PMC

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Grants and funding

The authors acknowledge support from Brazilian agencies CNPq, CAPES, and FUNCAP, the FUNCAP/Cnpq Pronex grant, and the National Institute of Science and Technology for Complex Systems in Brazil for financial support. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.