Figure 3
From: Scientific success from the perspective of the strength of weak ties
Illustration of the difference between symmetric and asymmetric neighbourhood overlap. In the figure, to highlight the benefits of analysing asymmetric overlaps, the corresponding values of: (a) symmetric \(O_{ij}\) (1) and (b, c) asymmetric \(Q_{ij}\ne Q_{ji}\) (2) overlaps have been calculated for the same network configuration, in which interconnected nodes differ in the size of their ego-networks. In such cases, which are typical for complex networks with underlying fat-tailed distributions, a common scenario is that for \(k_i\ll k_j\) one has \(Q_{ij}\gg Q_{ji}\simeq O_{ij}\). This explains why introducing tie direction is necessary for reliable verification of the Granowetter’s theory in scientific collaboration networks.
