کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
7375685 | 1480072 | 2018 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Relationships between Perron-Frobenius eigenvalue and measurements of loops in networks
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
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چکیده انگلیسی
The Perron-Frobenius eigenvalue (PFE) is widely used as measurement of the number of loops in networks, but what exactly the relationship between the PFE and the number of loops in networks is has not been researched yet, is it strictly monotonically increasing? And what are the relationships between the PFE and other measurements of loops in networks? Such as the average loop degree of nodes, and the distribution of loop ranks. We make researches on these questions based on samples of ER random network, NW small-world network and BA scale-free network, and the results confirm that, both the number of loops in network and the average loop degree of nodes of all samples do increase with the increase of the PFE in general trend, but neither of them are strictly monotonically increasing, so the PFE is capable to be used as a rough estimative measurement of the number of loops in networks and the average loop degree of nodes. Furthermore, we find that a majority of the loop ranks of all samples obey Weibull distribution, of which the scale parameter A and the shape parameter B have approximate power-law relationships with the PFE of the samples.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica A: Statistical Mechanics and its Applications - Volume 501, 1 July 2018, Pages 153-163
Journal: Physica A: Statistical Mechanics and its Applications - Volume 501, 1 July 2018, Pages 153-163
نویسندگان
Lei Chen, Yingxin Kou, Zhanwu Li, An Xu, Yizhe Chang,