Fig. 4.
Weak ties are optimally distributed. (A) Three modules identified at pc = 0.98 for the subject in Fig. 1B. The colors correspond to different submodules as identified by the box-covering algorithm at ℓB = 21. (B) When we lower the threshold to p = 0.975, weak ties connect the modules. The three original modules as they appear in A are plotted in red; orange, purple, and the light blue nodes are the nodes added from A as we lower p. Blue lines represent the added weak links with distance longer than 10 mm. The weak links collapse the three modules into one. (C) Sketch of the different critical values of the shortcut exponent α in comparison with df. (D) Cumulative probability distribution P(rij > r). The straight line fitting yields an exponent α - 1 = 2.1 ± 0.1 indicating optimal information transfer with wiring cost minimization (45). Certain clusters occupy two diametric parts of the brain. In practice, these are two modules that are connected through long-range links. These links increase significantly the percentage of links at large distances rij, because they are superimposed on top of the regular distribution of links within unfragmented clusters. This behavior is manifested as a bump in the curve.