Figure 1

(a) The distribution of words by their number of appearances in James Joyce’s Ulysses (empirical data). The numerical data was obtained from a single realization of Simon’s model with $p$ equal to the ratio of unique words (30 030) on the total word count (267 350). (b) Schematization of the systems considered in this Letter, illustrating how order (Simon’s model of balls in bins) and randomness (Barabási-Albert’s model of random networks) coexist in a spectrum of complex systems. (c) The distribution of coactors and movies per actor in the Internet Movie Database since 2000. The organization moves closer to a true power law when looking at a higher structural level (i.e., movies versus coactors).Reuse & Permissions

Figure 2

(top) Representation of the possible events in a step of node-based SPA; the probability of each event is indicated beneath it. (bottom) A schematization of the spectrum of systems obtainable with SPA. Here, we illustrate the conceptual differences between node-based $s=1$ and link-based systems $s=2$: Simon’s model ($q=1$) creates structures of size one (nodes), while the BA model ($p=q=1$) creates random networks through structures of size two (links).Reuse & Permissions

Figure 3

Circles: distributions of topological quantities for (a) the cond-mat arXiv circa 2005; (b) Internet at the level of autonomous systems circa 2007; (c) the IMDb network for movies released since 2000. Solid lines: average over multiple realizations of the SPA process with (a) $p=0.56$ and $q=0.59$; (b) $p=0.04$ and $q=0.66$; (c) $p=0.47$ and $q=0.25$. For each realization, iterations are pursued until an equivalent system size is obtained. The Internet data highlights the transition between exponential and scale-free regimes in a typical community degree distribution. It is represented by a single realization of SPA (dots), because averaging masks the transition.Reuse & Permissions