Abstract
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 according to probability 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, and , 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.
Highlights
Complex networks are acknowledged as an invaluable system for describing nature and society [1,2]; many endeavors have been devoted to exploring the structure and properties of complex networks for characterizing and simulating the properties of some real-world systems in our life
Watts and Strogatz put forward a small-world WS-model [9], which can rationally reflect the statistical properties of the network that are neither completely regular nor entirely random and explain small-world phenomena in various real-world networks by exploring the diameter and clustering coefficient
Let Ti be the mean first-passage time (MFPT) from node i to the (t) trap. h T it denotes the average trapping time (ATT), which is defined as the mean of Ti starting from all sources of nodes over the whole network to the trap node
Summary
Complex networks are acknowledged as an invaluable system for describing nature and society [1,2]; many endeavors have been devoted to exploring the structure and properties of complex networks for characterizing and simulating the properties of some real-world systems in our life. Among all of these properties, the scale-free nature, diameter, and clustering coefficient have attracted considerable attention [3–5]. We draw the conclusion with a concise narrative
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