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| Power Law Thinking Series 1—The Barabási Law and Pareto Law are Not Mutually Included |
| YAN Chun-ninga, SHAN Shib, SHI Ding-huac
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| a. School of Management; b. Center for Information Studies; c. School of Science, Shanghai University, Shanghai 200444, China |
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Abstract An important concept in complex networks is the degree distribution has a power-law tail. In order to determine the degree exponent of geometric growth networks, people need to use complementary degree distribution. Then, a theoretical problem is proposed: for discrete distributions, if complementary distribution has a power-law tail, distribution has a power-law tail, and vice versa. We found that this conclusion is not true in general. A necessary and sufficient condition that distribution and complementary distribution also has a power-law tail is given in this paper.
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Received: 28 October 2013
Published: 22 June 2026
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