Abstract
Although structure entropy is a useful method to measure the complexity of complex networks, there exist shortcomings, such as the limits of network scales and network types. By combining structure entropy and the absolute density of network, a method is improved to effectively measure the complexity of complex networks. For the improved measure, not only the topology of network is considered, but also the scales of network are considered, and the measurement of network complexity is not affected by the network scales and types. Moreover, the complexity of small-world networks, BA scale free networks, Sierpinski self-similarity networks, Erodos-Renyi (ER) random networks and six real networks (i.e., the 9/11 terrorist network, Celegans network, a USAir network, the USA Political blogs network, a collaboration network in science of networks (NetScience) and yeast protein interaction (YPI) network) are measured by employing the method. The results show that the improved method is effective and feasible to measure the complexity of complex networks.
Highlights
With the extensive study on complex network, such as smallworld network model [1], Newman and Watts proposed the NW network model [2], BA scale free network model [3], self-similarity network model [4] and ER random network model [5] etc., the complexity of complex network was researched by many scholars [6]–[10]
Besides the connectivity and density of network, entropy is a good tool for studying network information and topology uncertainty [28], which has been widely applied to measure the complexity of network [29]–[32], especially for the structure entropy
The reason is that the structure entropy is considered, and the absolute density of network is taken into account, the results showed that the proposed method is effective
Summary
With the extensive study on complex network, such as smallworld network model [1], Newman and Watts proposed the NW network model [2], BA scale free network model [3], self-similarity network model [4] and ER random network model [5] etc., the complexity of complex network was researched by many scholars [6]–[10]. Besides the connectivity and density of network, entropy is a good tool for studying network information and topology uncertainty [28], which has been widely applied to measure the complexity of network [29]–[32], especially for the structure entropy. For the different density and no weighted spacial structure network, the complexities of these networks could be not measured by the modified structure entropy in Ref. Seven constructed small-world networks, BA scale free networks, Sierpinski self-similarity networks, ER random networks, and six real networks are used to illustrate the proposed method.
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