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ݴ뿹

Small WorldģͿԷ֣֮жصļʣɴ˴Samll World϶ѧģ͵ʣȫΪ ˼ijӵԵʡˣSmall World磬ֻҪܹʶЩӣȻԳӽйͿں̶ܴ ıSmall WorldĽṹԶSmall WorldĹĹؼdzӵʶⲢһƽӹ⡣ڹ ĻϸõSmall World磬ֱǾܹʶ𳤳ӡѵ˳һͼdz̳ ӾͲˡǡǡʵʱֹڶ˳ʵϾDzڵġPanditAmritkar[40] оһ⣬һֻڸ·ıߵĽĶ壬ȻɱߵĽӳ䳤̻Ƕ̳ӡʶ𷽷 ܺõһܺõļ--ߵĽ--Ժܺõ𳤳̳̱ߡߵĽĺ·б뾭 ˱ߵĴһţ˲ͬļŵ֮·ͻᾭӡ֮ͬĶ ԵĿ C2n1+n2ԶԶڼڲĿ֮ C2n1 + C2n2 n1, n2ΪŶ ˿԰ѱߵĽΪжϳӵһַMotter˵[41]о˻ڱߵĽĹʽSmall World ĹʽdzСSmall World磬Ԥνṹܴıƽ̾䳤ˣƽ۳̶ȱСˡ ˣṹȶԵоһشĸŹı仯ۣƽ̾룬ƽ۳̶ȣŵԴС Źģֲģʽе»·ȴƽۣ̾Ϊƽ̾ŹȵӶӣЧʵͨ ෴·ȵĶ£

l-1 = $\displaystyle {\frac{{2}}{{N\left(N-1\right)}}}$$\displaystyle \sum$$\displaystyle {\frac{{1}}{{d_{ij}}}}$ (19)

һĹʽѡȥȥַʽѡķʽϷΪѡԹ[42]ֱΪ ݴ뿹о[42,43]Scale Free кǿݴԣǶڻڶĶֵѡԹϲڻڱߵĽĹҲdzСô ЩѡԹ֮ǷȼۣйնĶֵȥĵ밴նĽȥĵ֮ںǿĹԵĻ Ǿ˵ʵֹȼۡԽһоڱߵĽȥ߹ǰȥ㹥֮Ĺԡǿ⼸ ԵʱʵѾĽṹȶԻصľ̬ʡǿ԰նֵжȻǿٰ Ľ֮ںǿĹΪַʽȼۡɼĽṹȶľ̬Ҳǽ ϵһġ[43]̾ȼȥȥ㹥µĸı䣬˶ֵȼ ԡ

ʵĽṹȶԷһҪʵʳ硣ṹȶԵоڹͬ磨ÿ 㶼ͬѡԹЧ൱Small WorldڳӹdzУScale Free ǿ³ԣǻڶֵѡԹɺܴĽṹƻôʳأڹģƣʳĶ ֲûеõյоʷֲȷֲԼֲָȶʽϣֵ˥ ̬ϵͳʲôӰأDunne˵[57]о16ͬʳ ͻڶֵѡԹӦ50%ȥΪ³ԵĶ־Ľṹͬ ³ӵĽ̶ܳȾкǿǷͬScale Freeи ǿ³أУʳ磬ԶֵΪĹԷӳǷһԻڶĹ ʽأ

ṹȶһʵSARSȾĿơΪSARSȾھϴļӴ ȾҪʽ¥Ϊ㣬ԱΪӵľ硣ҵİ칫¥ͥסе㣬 ΪҵĴڣ֮佨ӡһӦðĹѧϰƷҪĻõȼ档 һ磬ϹڴȾĸϸĵ飬ǾͿ繥Ϊ۶ԴȾĿơ

ȣҪоĻṹƽ̾ƽ۳̶ȵȷֲȾ̬ʡȻص 봫ȾصƶԤжijЩӵķijЩ㣬ıʡΪȾ ĸư棬һǶԵòԱӴߵĸ룬ڶǶṹԤȸ룬ҲǶԽ˵Ĺѧϰ еڷֲ֮ǰصظijЩ޶ijЩڼҰ칫ȵȡޣĿǰûпչ ݵ鹤Scale FreeĹϴȾĿϵģоڽУǵĿҵScale Free һֹʹôģѸٴĴȾתΪСģ

ĿǰSARSȫ緶ΧйʡеУоһ͸нԺʵˡʵо֣ ѹϵ[7]Ի[47]һSmall WorldScale Free硣ϲʲô ʽʹȾеõƣĿǰһдо[64]

ϹøķƴȾû漰Ĵ⡣ʵھ߹УҪص㿼ǵ⡣ṹ ĽǶȷijһҪҪ룬ǴӾԼЧĽǶȿָܻᷢĴ۷dzʱҪ֮ȡ ƽ⡣ˣҪڿоͰѴ۰⿼֮ڡһ繥Ҳֵ۵ձ塣Ƕ ڶߵҪ̶ȣ

Costv $\displaystyle \sim$ kvorBv
Costl $\displaystyle \sim$ Bl
(20)
ȻǾͿоԼϵĴȾĴ۵Ĺϵڹ̶۵ŵĸ뷽ʽ ̶ܸ붥µĸ뷽ʽͬĽ

Чṹ빦ܹϵһҪɲ֡Ѫܵķ֧ΪˮѪҺĴ磬ṹ봫Ч ĹϵڷμεоѾõо[59]ʵķ֧ΪɣAllometric Scaling [59]֤ˣǶdάռδ磬Чµķ֧ϵΪ $ \eta$ = $ {\frac{{d+1}}{{d}}}$ ʳΪĴ磬Garlaschelli[58]оһ ĽṹЧʹϵȴʳԻΪڵһСеÿһ㣬ֱӵϼ ֱӲʳAi嶥ĺɢ Ci = $ \sum_{{k>i}}^{}$Akk > iĺiϼ㡣оCi AiĹϵ֣߳ɹϵ

C $\displaystyle \sim$ A$\scriptstyle \eta$. (21)
ңͬʳָͬ $ \eta$ = 1.13$ \pm$0.03ں $ \eta$ = $ {\frac{{2+1}}{{2}}}$ = 1.5Ѫ $ \eta$ = $ {\frac{{3+1}}{{3}}}$ = 1.33 ˵ͬʳѭͬŻ򡣵$ \eta$ = 1.13ܱΪάռеķ֧Ż $ \eta$ = $ {\frac{{d+1}}{{d}}}$ Ϊʳһһ磬ǶijһάŷϿռСɴҲһ⣬һ磬Ƿ άĺۼʡSmall Worldϵģ͵ʱֹ־ЧģͶѧʵĺ ʴڣôһζأԷѧϤĶ߿Է֣άģеơ ѧУģ͵ٽָеĿռάdһ㶼άdf棬άһͨνṹļ ϴЧģ͵оҲȷʵʾһļĴڡǹԼ䶨дڸӹ㷺 Ĺ϶ѧģԼо

ṹ빦ܹϵһҪصıЩֻͨ߼оĶϽŵ ۷֮һϵĶ֮ǴijЩŵġWWWУijһڵҳ໥ϵ󣬿ѧ дŶЩϻŶڲ֮ӻŶ֮ӸƵôֻҪļνṹڣǾ ͨṹϵķЩŶӣҪݡŶӦļνṹַʽһŶڲԱ֮ ۳̶ȻŶ֮ĸߡڶͬŶӵĶ֮·һҪӡӸȨĵȼ۷[6] Hierarchical ClusteringڵһNewman[73]ĻڱߵĽ۷ǰǵڶ ӸȨĻ˼ǣҵ֮··Լ··ʱֻȡ ·3ڵ·³Ϊl·nlͬһڵ㣬ڸ·ȻҪȲͬŵ ֮Ҫࡣ˶̶ܳ

S = $\displaystyle \sum$nl$\displaystyle \alpha^{{l}}_{}$ (22)
У$ \alpha$Ϊ $ \left(\vphantom{0, 1}\right.$0, 1$ \left.\vphantom{0, 1}\right)$֮ijһȻ̶ܳ۷ڽ۷ǼÿߵĽȥ ıߣȻټʣ±ߵĽȥıߣֱûбߣеȥߵḶ́Ǹɼ ˳򡣶ʵϵͳʱַͬĽʱͬΪǻڲͬļ裬˵ĸһЩϰ ·ĸȨ⣬·ȨֻǶ·ֻԻر·ĸȨЩ෽ ϵдо϶صķӦҲоҪɲ֡


wwwwjs 2004-01-04