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How to become a superhero

Pablo M Gleiser

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Figure 1

Figure 1. Mean degree \langle k_{\mathrm {nn}} \rangle of the neighbors of a vertex as a function of the degree k. Circles show the different values of knn for a given k. The continuous line indicates the average value \langle k_{\mathrm {nn}} \rangle
.



Figure 2

Figure 2. Weight distribution P(w) versus w (circles). The straight line is a power law fit, P(w) ~ w–2.26.



Figure 3

Figure 3. (a) Network after the addition of 220 links. The initials correspond to characters that play an important role connecting communities: Spider-Man (SM), Thing (T), Beast (B), Captain America (CA), Namor (N), Hulk (H). (b) Network after the addition of 300 links, when a giant component has emerged. The black (white) circles indicate characters labeled as heroes (villains). The gray circles indicate other types of characters, such as people, gods or nodes with no classification.



Figure 4

Figure 4. Fraction of sites in the largest component fslc as a function of the number of links added in decreasing weight order. The inset shows in detail the transition between 200 and 300 links.



Figure 5

Figure 5. Fraction of sites in the largest component fslc as a function of the number of links added when the links are chosen in decreasing weight order (circles) and also when they are chosen in random order (squares). The inset presents a detail for short times in a log–log plot. The dashed line shows the power law decay 1/x as a guide to the eye.



Figure 6

Figure 6. Clustering C(k) as a function of the degree k. The dashed line shows the power law 1/k as a guide to the eye.




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