In this paper, on condition that the word frequency follows the quasi power-law distribution and contents densification, it is proven that the Zipf’s law and Heaps law are equivalent, and critical behavior when γ=2 is also discussed.
YAN Chunning
,
SHAN Shi
,
SHI Dinghua
. Power Law Thinking Series 4—Equivalent Condition of Heaps Law and Zipf Law[J]. Complex Systems and Complexity Science, 2014
, 11(4)
: 1
-3
.
DOI: 10.13306/j.1672-3813.2014.04.001
[1] Zipf G K. Human Behaviour and the Principle of Least Effort:An Introduction to Human Ecology[M]. Cambridge:Addison-Wesly, 1949.
[2] Heaps H S. Information Retrieval:Computational and Theoretical Aspects[M]. Orlando:Academic Press, 1978.
[3] Lü L Y, Zhang Z K, Zhou T. Zipf’s law leads to Heaps’ law:analyzing their relation in finite-size systems[J]. PLoS ONE, 2010, 5（12):e14139.
[4] 阎春宁,山石,史定华. 冥律思考系列文章1——论Barabási律与Pareto律互不包含[J]. 复杂系统与复杂性科学, 2014, 11（1):1-5.
Yan Chunning, Shan Shi, Shi Dinghua. Power law thinking series 1—the Barabási law and Pareto law are not mutually included[J]. Complex Systems and Complexity Science,2014,11（1):1-5.
[5] Shi D H. Theory of Network Degree Distribution[M]. Beijin:Higher Education Press, 2011.
