Figure
5 displays the behavior of the average degree of nodes inside the largest $\langle {K}_{\max }\rangle $ (solid lines) and second largest 〈
K2〉 (dashed lines) nucleating clusters as a function of order parameter
λ. It is clear that, without activity, $\langle {K}_{\max }\rangle $ for different networks, always increase from lower values, and gradually approaches the average node degree 〈
k〉 of the network, which means that nucleation starts from nodes with small degree. However, activity plays different roles in the nucleation pathways for different network topologies. For a small world network, $\langle {K}_{\max }\rangle $ also increases from a lower value (red solid line), and close to 〈
k〉, but it grows faster than that without activity. It is worth noting that 〈
K2〉 is almost run in parallel with $\langle {K}_{\max }\rangle $ up to a critical nucleus coming into being. Beyond the critical nucleus 〈
K2〉 decreases gradually, and $\langle {K}_{\max }\rangle $ increases, as indicated by the red line in figure
5(a). This implies that hub nodes are separated into different nucleating clusters by activity, thereby inhibiting the growth of nucleus. For random network, nodes with high degrees that are connected with the largest nucleus are more likely to be pulled into the nucleating cluster, this is because that the probability of these nodes being moved is larger than other lower degree nodes. As a result, a jump of $\langle {K}_{\max }\rangle $ in the active model is observed at first, as shown in figure
5(b), and then it approaches to 〈
k〉. Meanwhile, 〈
K2〉 decreases rapidly, which accelerates the growth of the largest nucleating cluster. For BASF network, since hub nodes are often connected with many small degree nodes, nucleation thus begins with small degree nodes and almost together with hub nodes being connected with new phase nodes through activity. Therefore, it turns out that, at the very beginning of nucleation, both $\langle {K}_{\max }\rangle $ and 〈
K2〉 are larger than 〈
k〉, which is significantly different from the observation in the inactive case. Nevertheless, with proceeding of nucleation, $\langle {K}_{\max }\rangle $ decreases rapidly and approaches to 〈
k〉 eventually, as shown in figure
5(c).