Figure 2
Effect of indirect utility on the structure of the networks formed by the utility-based preferential attachment model. (a) An illustration of a network formed by the respective UR, UD, and UI models at \(t=5000\). The red colour represents the local hub, which is a node with \({k}_{i}^{\left[1\right]}\) greater than the surrounding nodes, and it is displayed in blue gradually according to the distance from the nearest local hub. In UI model, a converged and hierarchical structure forms in which many nodes grow sequentially around a very large local hub. (b,c) The distribution \(P(k^{[1]})\) and the growth of the ratio \(\overline{{k}^{\left[2\right]}}(t)(\equiv {\sum }_{{{j}}=1}^{{{t}}}{{{k}}}_{{{j}}}^{\left[2\right]}({{t}})/{\sum }_{{{j}}=1}^{{{t}}}{{{k}}}_{{{j}}}^{\left[1\right]}({{t}}))\) in the utility-based preferential attachment models. The solid line represents the average of 20 numerical simulations (\(t=100,000\)), and the error bar denotes the standard deviation.
