Parameter specification for the degree distribution of simulated Barabási-Albert graphs

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• 作者：Fairul Mohd-Zaid^a ; ^{fairul.mohd-zaid@us.af.mil" class="auth_mail" title="E-mail the corresponding author} ; Christine M. Schubert Kabban^a ; Richard F. Deckro^b ; Edward D. White^a
• 关键词：Barabá ; si&ndash ; Albert ; Degree distribution ; Parameter estimation ; Pareto distribution ; Yule&ndash ; Simon distribution ; Goodness of fit
• 刊名：Physica A: Statistical Mechanics and its Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：465
• 期：Complete
• 页码：141-152
• 全文大小：1981 K

文摘

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d="p000005">Least squares method is not appropriate for estimating d="mmlsi63" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0378437116304551&_mathId=si63.gif&_user=111111111&_pii=S0378437116304551&_rdoc=1&_issn=03784371&md5=44be2b539ba87f104e9f0d53ed05bdf5">mg class="imgLazyJSB inlineImage" height="14" width="9" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0378437116304551-si63.gif">mathContainer hidden">mathCode"><math altimg="si63.gif" overflow="scroll"><mstyle mathvariant="normal"><mi>βmi>mstyle>math> of Barabási&ndash;Albert graphs.

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d="p000010">A modified version of Clauset et al. (2009) is more preferable for estimation.

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d="p000015">Simulated graphs show that exponent is not the theoretical d="mmlsi64" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0378437116304551&_mathId=si64.gif&_user=111111111&_pii=S0378437116304551&_rdoc=1&_issn=03784371&md5=ad32e01cf5125f1d3c4c81128b63c604">mg class="imgLazyJSB inlineImage" height="14" width="40" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0378437116304551-si64.gif">mathContainer hidden">mathCode"><math altimg="si64.gif" overflow="scroll"><mstyle mathvariant="normal"><mi>β = 2mi>mstyle>math> for small graphs.

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d="p000020">Value of d="mmlsi63" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0378437116304551&_mathId=si63.gif&_user=111111111&_pii=S0378437116304551&_rdoc=1&_issn=03784371&md5=44be2b539ba87f104e9f0d53ed05bdf5">mg class="imgLazyJSB inlineImage" height="14" width="9" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0378437116304551-si63.gif">mathContainer hidden">mathCode"><math altimg="si63.gif" overflow="scroll"><mstyle mathvariant="normal"><mi>βmi>mstyle>math> is also dependent on number of edges added, d="mmlsi21" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0378437116304551&_mathId=si21.gif&_user=111111111&_pii=S0378437116304551&_rdoc=1&_issn=03784371&md5=c7e82b1375e888385c12dfdbc76f3214" title="Click to view the MathML source">mmathContainer hidden">mathCode"><math altimg="si21.gif" overflow="scroll"><mi>mmi>math>, for small graphs.

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d="p000025">Smaller value of m results in larger value of d="mmlsi63" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0378437116304551&_mathId=si63.gif&_user=111111111&_pii=S0378437116304551&_rdoc=1&_issn=03784371&md5=44be2b539ba87f104e9f0d53ed05bdf5">mg class="imgLazyJSB inlineImage" height="14" width="9" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0378437116304551-si63.gif">mathContainer hidden">mathCode"><math altimg="si63.gif" overflow="scroll"><mstyle mathvariant="normal"><mi>βmi>mstyle>math> for all graph sizes.

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