The Structure and First-Passage Properties of Generalized Weighted Koch Networks

Characterizing the topology and random walk of a random network is difficult because the connections in the network are uncertain. We propose a class of the generalized weighted Koch network by replacing the triangles in the traditional Koch network with a graph R-s according to probability 0 <= p <= 1 and assign weight to the network. Then, we determine the range of several indicators that can characterize the topological properties of generalized weighted Koch networks by examining the two models under extreme conditions, p = 0 and p = 1, including average degree, degree distribution, clustering coefficient, diameter, and average weighted shortest path. In addition, we give a lower bound on the average trapping time (ATT) in the trapping problem of generalized weighted Koch networks and also reveal the linear, super-linear, and sub-linear relationships between ATT and the number of nodes in the network.

Automated summary

This study proposes a generalized weighted Koch network to characterize the topology and random walk of a random network. By replacing the triangles in the traditional Koch network with a probability graph R-s and assigning weights, the range of several indicators that can characterize the topological properties of the generalized weighted Koch network is determined. In addition, the average trapping time (ATT) in the trapping problem of the generalized weighted Koch network is analyzed, revealing the linear, super-linear, and sub-linear relationships between ATT and the number of nodes in the network.