䝛䝑䝖䝽䞊䜽䛸䛿 䠊䠊䠊኱Ꮫ㝔ඹ㏻ᤵᴗ⛉┠䛂䝖䝫䝻䝆䞊⌮ᕤᏛ≉ูㅮ⩏ 䠥 䠖⛉Ꮫ䛸䝖䝫䝻䝆䞊䛃䝛䝑䝖䝽䞊䜽䝖䝫䝻䝆䞊ᙐᩃȍȃȈȯȸǯƷወᚘႎࣱឋ䝜䞊䝗໭ᾏ㐨኱Ꮫ ᕤᏛ◊✲㝔 ᛂ⏝≀⌮Ꮫ㒊㛛▮ஂಖ ⪃௓䝸䞁䜽ࣀ࣮ࢻ㸸 ሙᡤ䚸ே䚸≀䚸ゝⴥ䚸ᴫᛕ䚸䞉䞉䞉ࣜࣥࢡ㸸 䝜䞊䝗䛸䝜䞊䝗䛾㛵ಀ䝛䝑䝖䝽䞊䜽䛾౛䠍䠖 ᆅୗ㕲䝛䝑䝖䝽䞊䜽ᵝ䚻䛺䝛䝑䝖䝽䞊䜽䝜䞊䝗䠖㥐䝸䞁䜽䠖㊰⥺䝛䝑䝖䝽䞊䜽䝜䞊䝗䝸䞁䜽䜲䞁䝍䞊䝛䝑䝖䝁䞁䝢䝳䞊䝍㏻ಙᅇ⥺㼃㼃㼃㼃㼑㼎䝨䞊䝆䝸䞁䜽┦஫స⏝㟁Ꮚ䜽䞊䝻䞁┦஫స⏝ேⓗ䝁䝭䝳䝙䜿䞊䝅䝵䞁 ே཭ே㛵ಀ䚸ᩛᑐ㛵ಀ

஺㏻⥙✵㊰⥺ᫎ⏬ತඃ䝛䝑䝖䝽䞊䜽ᫎ⏬ತඃඹ₇㛵ಀㄽᩥඹⴭ◊✲⪅ඹⴭ㛵ಀㄽᩥᘬ⏝ㄽᩥᘬ⏝㛵ಀ༢ㄒ䝛䝑䝖䝽䞊䜽༢ㄒᩥ୰䛻㞄᥋䠄ḟ㞄᥋䠅䛧䛶఩⨨䛩䜛䝛䝑䝖䝽䞊䜽䛾౛䠎䠖 䝁䞁䝢䝳䞊䝍䞉䝛䝑䝖䝽䞊䜽䝜䞊䝗䠖䝁䞁䝢䝳䞊䝍䝸䞁䜽䠖ᅇ⥺䝛䝑䝖䝽䞊䜽䛾౛4䠖 WWW䝜䞊䝗䠖Web䝨䞊䝆䝸䞁䜽䠖䝝䜲䝟䞊䝸䞁䜽䝛䝑䝖䝽䞊䜽䛾౛3䠖 䜲䞁䝍䞊䝛䝑䝖䝜䞊䝗䠖䝁䞁䝢䝳䞊䝍䝸䞁䜽䠖≀⌮ᅇ⥺䝛䝑䝖䝽䞊䜽䛾౛5䠖 ༢ㄒ䛾䝛䝑䝖䝽䞊䜽䝜䞊䝗䠖༢ㄒ䝸䞁䜽䠖ᩥ❶୰䛷㞄䜚ྜ䛖䛛୍䛴㣕䜀䛧䛻㞄䜚ྜ䛖㛵ಀ
kingyellowtypelandrace

poem
apple

MARCELLUS Good now, sit down, and tell me, he that knows, Why thishistory
same strict and most observant watch So
nightly toils the subject of the land, And why such daily cast of brazen cannon, And foreign mart for implements of war;
Why such impress of shipwrights, whose sore task Does not divide the Sunday from the week; What might be toward,
jobjoint-labourer with the day: Who is't that can inform me?
that this sweaty haste Doth make the night
HORATIO That can I; At least, the whisper goes so. Our last king, Whose image even but now appear'd to us, Was, asblood
you know, by Fortinbras of Norway, Thereto prick'd on by a most emulate
in which ourmanpride, Dared to the combat;
valiant Hamlet-- For so this side of our known world esteem'd him-- Did slay this Fortinbras; who by a seal'd compact,
Well ratified by law and heraldry, Did forfeit, with his life, all those his lands Which he stood seized of, to the conqueror:
Against the which, a moiety competent Was gaged by our king; which had return'd To the inheritance of Fortinbras, Had
he been vanquisher; as, by the same covenant, And carriage of the article design'd, His fell to Hamlet. Now, sir, young
Fortinbras, Of unimproved mettle hot and full, Hath in the skirts of Norway here and there Shark'd up a list of lawlessresolutes, For food and diet, to some enterprise That hath a stomach in't; which is no other-- As it doth well appear unto
our state-- But to recover of us, by strong hand And terms compulsatory, those foresaid lands So by his father lost: andthis, I take it, Is the main motive of our preparations, The source of this our watch and the chief head Of this post-haste
and romage in the land.

䝛䝑䝖䝽䞊䜽䛾౛6䠖㓝ẕ䛻䛚䛡䜛䝍䞁䝟䜽㉁㛫┦஫స⏝䝛䝑䝖䝽䞊䜽䝜䞊䝗䠖⺮ⓑ㉁䝸䞁䜽䠖┦஫స⏝䝛䝑䝖䝽䞊䜽䛾౛7䠖 ⛉Ꮫㄽᩥඹⴭ㛵ಀ䝛䝑䝖䝽䞊䜽䝜䞊䝗䠖◊✲⪅䝸䞁䜽䠖ඹⴭ㛵ಀ䝛䝑䝖䝽䞊䜽䛾୍⯡ⓗᛶ㉁䝛䝑䝖䝽䞊䜽䛻㛵䛩䜛⌮ㄽⓗᢅ䛔䠙䖃䝛䝑䝖䝽䞊䜽ᵓ㐀䛻㊥㞳䛾ᴫᛕ䛿䛺䛔䜾䝷䝣⌮ㄽྠ䛨ᵓ㐀䠄䠍䠔ୡ⣖䛾䜸䜲䝷䞊䜢๰ጞ⪅䛸䛩䜛ᩘᏛ䠖䝖䝫䝻䝆䞊䛾㉳※䠅

⭾኱䛺䝜䞊䝗ᩘ䜢䜒䛴」㞧䛺䝛䝑䝖䝽䞊䜽䖃㐃⤖ᛶ䛜ኚ䜟䜜䜀ᵓ㐀䛿ኚ䜟䜛␗䛺䜛ᵓ㐀」㞧䝛䝑䝖䝽䞊䜽⛉Ꮫ䠄」㞧䝛䝑䝖䝽䞊䜽䛾⤫ィⓗᛶ㉁䜢ゎ᫂䛩䜛䠅1998䡚㐃⥆ኚᙧ䛧䛶䜒⧅䛞᭰䛘䛜䛺䛡䜜䜀ྠ䛨ᵓ㐀䝖䝫䝻䝆䞊䝛䝑䝖䝽䞊䜽䜢≉ᚩ௜䛡䜛ᵝ䚻䛺㔞䖃 䜽䝷䝇䝍䞊ಀᩘ C䖃 ⥲䝜䞊䝗ᩘ N䝛䝑䝖䝽䞊䜽䛾䝃䜲䝈䖃 ⥲䝸䞁䜽ᩘ n䝜䞊䝗 i 䛛䜙ฟ䛶䛔䜛䝸䞁䜽ᩘ䖃 䝜䞊䝗䛾ḟᩘ ki䖃 ᖹᆒḟᩘ <k>
k1
¦ ki
N i

2n

䝜䞊䝗 i 䛾㏆᥋䝜䞊䝗ᩘkii㏆᥋䝜䞊䝗䛜஫䛔䛻䝸䞁䜽䛩䜛⤌䜏ྜ䜟䛫䛾ᩘ : Sik N䖃 䝜䞊䝗㛫㊥㞳 djSi䝜䞊䝗ᑐ䜢⤖䜆䝸䞁䜽ᩘ䛾᭱ᑠ್d iji

䝜䞊䝗 i 䛾ḟᩘkii

ki

C2ki (ki  1)
2

㏆᥋䝜䞊䝗䛜ᐇ㝿䛻䝸䞁䜽䛧䛶䛔䜛ᩘ 䠖 Ei

䝜䞊䝗 i 䛾䜽䝷䝇䝍䞊ಀᩘ 䠖 Ci

2䖃 䝛䝑䝖䝽䞊䜽ᚄ l䝛䝑䝖䝽䞊䜽ෆ䛾඲䛶䛾䝜䞊䝗㛫㊥㞳䛾᭱኱್䖃 ᖹᆒ䝜䞊䝗㛫㊥㞳 <d>䝛䝑䝖䝽䞊䜽ෆ䛾඲䛶䛾䝜䞊䝗㛫㊥㞳䛾ᖹᆒ್Ci

EiSi᏶඲䜾䝷䝣
C=1

2 Ei
ki (ki  1)䝛䝑䝖䝽䞊䜽䛾䜽䝷䝇䝍䞊ಀᩘ 䠖 CC䝒䝸䞊ᵓ㐀
C=0CiC䛿䝛䝑䝖䝽䞊䜽䛜䛹䛾⛬ᗘᐦ䛻⧅䛜䛳䛶䛔䜛䛛䜢⾲䛩㔞䠎䠊䝇䜿䞊䝹䝣䝸䞊ᛶከ䛟䛾⌧ᐇ䝛䝑䝖䝽䞊䜽䛻ඹ㏻䛾ᛶ㉁ḟᩘ ki 䛾ศᕸ㛵ᩘ䛜䝧䜻㛵ᩘ䠍䠊䝇䝰䞊䝹䝽䞊䝹䝗ᛶ䝛䝑䝖䝽䞊䜽䝃䜲䝈N䛻ẚ䜉䛶ᖹᆒ䝜䞊䝗㛫㊥㞳䛜ᅽಽⓗ䛻ᑠ䛥䛔㧗䛔䜽䝷䝇䝍䞊ᛶl v ln N(A) ತඃ䛾ඹ₇㛵ಀ䚸(B) WWW䚸(C) 㟁ຊ⥙

C |0C |1ㄽᩥ䛾ඹⴭ㛵ಀ䚹(M)ᩘᏛ䚸(NS)⚄⤒⛉Ꮫ䝧䜻ศᕸྵܱƷȍȃȈȯȸǯƷșǭЎࠋP(k ) v kJ(k !! 1)

䠏䠊䝣䝷䜽䝍䝹ᛶࣇࣛࢡࢱࣝ㸻⮬㌟ࡢ୍㒊ศ࡜┦ఝ࡞ᵓ㐀㸦⮬ᕫ┦ఝ㸧㸻≉ᚩⓗ㛗ࡉࡀ↓࠸ᵓ㐀ǹǱȸȫȕȪȸࣱ 䠄≉ᚩⓗ䛺k䛜Ꮡᅾ䛧䛺䛔䠅
䃒=2.1
䃒=2.4
䃒=2.1
䞉䞉䞉

(WWW)
(Internet)
(NS)

ȏȖನᡯ
ᕧ኱䛺䝸䞁䜽ᩘ䜢ᣢ䛴䝜䞊䝗䠄䝝䝤䠅䛜ᑡᩘ䛺䛜䜙Ꮡᅾ䛩䜛䝣䝷䜽䝍䝹ᵓ㐀䛸䝣䝷䜽䝍䝹ḟඖ䠖l1⮬↛⏺䛾⮳䜛䛸䛣䜝䛻㐢ᅾ㌟䛾ᅇ䜚䛾」㞧䝛䝑䝖䝽䞊䜽䛿䝣䝷䜽䝍䝹䛛䠛N v l DCl2

䝛䝑䝖䝽䞊䜽㊥㞳 lB 䛾䝃䝤䜾䝷䝣䛷⿕そ䛩䜛䛾䛻ᚲせ䛺䝃䝤䜾䝷䝣䛾᭱ᑠᩘ NB䝃䜲䝈 l 䛾⟽䛻ྵ䜎䜜䜛㉁㔞 N 䠄 ᗘ䠅N B v l B D

N B v l B DB
䝃䜲䝈 lB 䛾⟽䛷⿕そ䛩䜛䛾䛻ᚲせ䛺᭱ᑠ䛾⟽䛾ᩘ NBlB

D 䞉䞉䞉 䝣䝷䜽䝍䝹ḟඖ䠄㠀ᩚᩘ䠅䝣䝷䜽䝍䝹lBNB64

⺮ⓑ㉁┦஫స⏝䝛䝑䝖䝽䞊䜽WWW䛸ತඃ䛾䝛䝑䝖䝽䞊䜽N B v l B D䝣䝷䜽䝍䝹䞉䝛䝑䝖䝽䞊䜽N B v l B D䝣䝷䜽䝍䝹䞉䝛䝑䝖䝽䞊䜽"Self-similarity of complex networks"
C. Song, S. Havlin, and H. A. Makse
Nature 433, 392 (2005).

⣽⬊ෆ⏕໬Ꮫ⤒㊰䝛䝑䝖䝽䞊䜽䜲䞁䝍䞊䝛䝑䝖

⺮ⓑ㉁┦஫స⏝䝛䝑䝖䝽䞊䜽N B v l B D

N B v exp(l B / l0 )䝣䝷䜽䝍䝹䞉䝛䝑䝖䝽䞊䜽㠀䝣䝷䜽䝍䝹䞉䝛䝑䝖䝽䞊䜽䝇䝰䞊䝹䝽䞊䝹䝗ᛶ䛾㉳※Watts-Strogatz 䠄1998䠅ከ䛟䛾⌧ᐇ䝛䝑䝖䝽䞊䜽䛻ඹ㏻䛾ᛶ㉁つ๎ᛶ䛸䝷䞁䝎䝮ᛶ䛾୧᪉䜢ྲྀ䜚ධ䜜䛯䝛䝑䝖䝽䞊䜽䞉䝰䝕䝹䛻䜘䜚኱䛝䛺䜽䝷䝇䝍䞊ಀᩘ䛸ᑠ䛥䛺䝛䝑䝖䝽䞊䜽ᚄ䜢୧❧䛥䛫䛯䚹䠍䠊䝇䝰䞊䝹䝽䞊䝹䝗ᛶ䠎䠊䝇䜿䞊䝹䝣䝸䞊ᛶ䠏䠊䝣䝷䜽䝍䝹ᛶ(1)ึ䜑䛻Nಶ䛾䝜䞊䝗䛛䜙䛺䜛䝸䞁䜾≧䛾᱁Ꮚ䜢⪃䛘䚸䝜䞊䝗㛫䛿Kಶ䛾᭱㏆᥋(N>>K>>lnN)䜎䛷⤖ྜ䛧䛶䛔䜛䚹䠄つ๎ᛶ䠅
N=83( K  2)
K=4C

඲䛶䛾⌧ᐇ䝛䝑䝖䝽䞊䜽䛜䛣䜜䜙䛾ᛶ㉁䜢
ඹ᭷䛧䛶䛔䜛䜟䛡䛷䛿䛺䛔䟿4( K  1)(2) ☜⋡p䛷䝷䞁䝎䝮䛻䝸䞁䜽䛾⧅䛞᭰䛘䜢䛩䜛䚹䛯䛰䛧䚸஧㔜䝸䞁䜽䜔⮬ᕫ䝸䞁䜽䜢⚗Ṇ䛩䜛䚹䠄䝷䞁䝎䝮䝛䝇䠅ఱᨾ䚸䛣䛾䜘䛖䛺ඹ㏻ᛶ䛜Ꮡᅾ䛩䜛䛾䛛䠛䜽䝷䝇䝍䞊ಀᩘ

K>>1p=0䛷䛾䜽䝷䝇䝍䞊ಀᩘC (0)3( K  2)
4( K  1)(1  p )3ᖹᆒ䝜䞊䝗㛫㊥㞳

lf (u )

3
4
NKKN
ln N
ln Kl3( K  2)
(1  p )34( K  1)ḟᩘศᕸ㛵ᩘf (k ,K )N 1/ df ( pKN )K4u  4u2

p=1

C䛾䠏ゅᙧ䛜䠏ゅᙧ䛾䜎䜎䛷䛔䜙䜜䜛☜⋡C ( p)

p=0tanh 1uu  4u
2P(k )¦n 0f (u )䝇䝰䞊䝹䝽䞊䝹䝗ᛶ­ const. u  1®
¯ln(u ) / u u !! 1

K /2

Cn (1  p ) n p K / 2 n( pK / 2) k  K / 2 n  pK / 2e(k  K / 2  n)!

䝷䞁䝎䝮䞉䝛䝑䝖䝽䞊䜽䛸
ᮏ㉁ⓗ䛻ྠ䛨኱䛝䛺 C 䛸ᑠ䛥䛺 l !

䝇䜿䞊䝹䝣䝸䞊ᛶ䛾㉳※

Barabasi-Albert 䝰䝕䝹

Barabasi-Albert 䝰䝕䝹䠄1999䠅ᡂ㛗䛸ඃඛⓗ㑅ᢥ䛾䝯䜹䝙䝈䝮䛻䜘䜚䝇䜿䞊䝹䞉䝣䝸䞊ᛶ䜢᭷䛩䜛䝛䝑䝖䝽䞊䜽䞉䝰䝕䝹䛾ᵓ⠏䛻ᡂຌ䚹(1) ึ䜑䛻m0 ಶ䠄ᑡᩘ䠅䛾䝜䞊䝗䛜Ꮡᅾ䛧䛶䛔䜛䚹ྛ᫬㛫䝇䝔䝑䝥䛷䠍ಶ䛾䝜䞊䝗䜢ຍ䛘䜛䚹䛣䛾䝜䞊䝗䛿m(䍺m0)ᮏ䛾䝸䞁䜽䜢ᣢ䛳䛶䛚䜚䚸᪤Ꮡ䛾䝜䞊䝗䛾䛹䜜䛛䛸⤖ྜ䛩䜛䚹䠄ᡂ㛗䠅(2) ᪂䛧䛟ຍ䜟䜛䝜䞊䝗䛜᪤Ꮡ䛾䝜䞊䝗䛸䝸䞁䜽䛷⤖䜀䜜䜛☜⋡䛿䚸

3 ( ki )2/6
3/10ki¦ ki

3/10
2/62/10i䛷୚䛘䜙䜜䜛䚹䠄ඃඛⓗ㑅ᢥ䠅

2/62/10䝝䝤ᵓ㐀䝣䝷䜽䝍䝹ᛶ䛾㉳※䖃 䝛䝑䝖䝽䞊䜽ᚄln Nl|ln ln N䝇䜿䞊䝹䞉䝣䝸䞊ᛶ䠄䝇䝰䞊䝹䝽䞊䝹䝗ᛶ䠅䖃 䜽䝷䝇䝍䞊ಀᩘ䝷䞁䝎䝮䞉䝛䝑䝖䝽䞊䜽䛸ྠ⛬ᗘ⌧ᐇ䛾䝛䝑䝖䝽䞊䜽䛸୙୍⮴Song el at. (Nature, 2005)」㞧䝛䝑䝖䝽䞊䜽䛻䝣䝷䜽䝍䝹ᛶ䛜䛒䜛䛣䛸䜢ⓎぢDCN vll v log N䠄䝣䝷䜽䝍䝹ᛶ䠅䠄䝇䝰䞊䝹䝽䞊䝹䝗ᛶ䠅

N B v l B DB
Yook el at. (PRL, 2005)
䝣䝷䜽䝍䝹䝛䝑䝖䝽䞊䜽䛿disassortative
Goh el at. (PRL, 2006)
䝣䝷䜽䝍䝹䞉䝛䝑䝖䝽䞊䜽䛾䝇䜿䝹䝖䞁ᵓ㐀䛿⮫⏺ⓗSong el at. (Nature Phys., 2006)
䝰䞊䝆䝳䞊䝹䛾ධ䜜Ꮚᵓ㐀䛥䜙䛺䜛䝛䝑䝖䝽䞊䜽䞉䝰䝕䝹䛾ᚲせᛶ䝣䝷䜽䝍䝹ᛶ䛾㉳※䛿?㐺ᛂᗘ䝰䝕䝹䛻䛚䛡䜛⮫⏺ⓗᛶ㉁䛸䝣䝷䜽䝍䝹ᛶ䝣䝷䜽䝍䝹ᵓ㐀㻌≉ᚩⓗ㛗䛥䛾↓䛔ᨭ㓄᪉⛬ᘧᖹ⾮⣔⮫⏺⌧㇟㠀ᖹ⾮⣔ ⮬ᕫ⤌⧊໬⮫⏺ᛶ (SOC)'I 0

N=2000N=4000N=6000N=8000N=10000

15.0䛒䜛䝟䝷䝯䞊䝍䃐䛻ᑐ䛩䜛┦㛵㛗

10.0㻌

⮫⏺⌧㇟

Average node-pair distance (lNP)

20.0

䃐=0.26 (=䃐c) 䛜⮫⏺Ⅼ

5.0

0.0
0.0

0.5

D

1.0

1.5

0.5Pc(s)M

1.0At䃐=䃐c10

3102101100-110

D/Dc⛛ᗎኚᩘ

410

0.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0䝣䝷䜽䝍䝹䞉䝛䝑䝖䝽䞊䜽䛾ᙧᡂ

100101s102䜽䝷䝇䝍䞊䞉䝃䜲䝈ศᕸ䝣䝷䜽䝍䝹ᛶ䛸䝇䝰䞊䝹䝽䞊䝹䝗ᛶ䛸䛾㛵ಀ㻌
310210Box-covering㏻ᖖ䛾⮫⏺⌧㇟

Cluster-growing」㞧䝛䝑䝖䝽䞊䜽䛾⮫⏺⌧㇟

21

10010 01001011010 0102lB101210䝣䝷䜽䝍䝹

䝣䝷䜽䝍䝹

DDd
䝴䞊䜽䝸䝑䝗

log N B

1log N B

10Nc

NB

10d of
 lB / l0䝇䝰䞊䝹䝽䞊䝹䝗 N B v elc䝛䝑䝖䝽䞊䜽䛿⮫⏺Ⅼ䛷䝣䝷䜽䝍䝹ᵓ㐀

DB

DC

1.77

log lBlog lB

」㞧䝛䝑䝖䝽䞊䜽䛾⛉Ꮫ䛾ᒎ㛤䖃 䝇䜿䞊䝹䝣䝸䞊ᛶ䛸䝇䝰䞊䝹䝽䞊䝹䝗ᛶ䖃 SF䚸SW䚸䝣䝷䜽䝍䝹ᛶ䛾┦஫㛵ಀ▱ே䝰䝕䝹
J. Davidsen et al.: Phys. Rev. Lett. 99, 128701 (2002).

䝇䜿䞊䝹䝣䝸䞊ᛶ㜈್䝰䝕䝹ྠ᫬ᡂ❧䛩䜛
䝰䝕䝹䛿䠛

呍呍
呍

M. Boguna et al.: Phys. Rev. E 68, 036112 (2003).

䃒䛸D䛻㛵ಀ䛜䛒䜛䛛䖃 䝇䜿䞊䝹䝣䝸䞊ᛶ䛸䝣䝷䜽䝍䝹ᛶ䝣䝷䜽䝍䝹ᛶ䝇䝰䞊䝹䝽䞊䝹䝗ᛶ⧞䜚㎸䜎䜜䛯䝜䞊䝗䛾ḟᩘk’䛸䛭䛾䝜䞊䝗䛾⧞䜚㎸䜏๓䛾䝜䞊䝗㞟ྜ䛾᭱኱ḟᩘk䛜ẚ౛䛧䚸ẚ౛ಀᩘ䛜⧞䜚㎸䜏䝃䜲䝈䛾dk஌䛻ẚ౛䛩䜛䝇䜿䞊䝹䝣䝸䞊䛺䝣䝷䜽䝍䝹䞉䝛䝑䝖䝽䞊䜽䛾ሙྜ䚸J 1
䜽䝻䝇䜸䞊䝞䞊

DBdkཧ⪃᭩䛭䛾௚䛾ၥ㢟୍⯡᭩䖃 ⮬ᕫ⤌⧊໬⮫⏺䛻䜘䜛」㞧䝛䝑䝖䝽䞊䜽ᙧᡂఱᨾ⌧ᐇ䛾䝛䝑䝖䝽䞊䜽䛜䝣䝷䜽䝍䝹ᵓ㐀䜢ྲྀ䜛䛛䠛䖃 㔜䜏௜䛡䜙䜜䛯䝛䝑䝖䝽䞊䜽䛾ᛶ㉁
0.3

4. 3

1 .5

0.
1

2.1

⯟✵㊰⥺䝛䝑䝖䝽䞊䜽ᰴ౯䛾┦㛵䝛䝑䝖䝽䞊䜽
⾑⟶⥙
䞉䞉䞉䞉

䖃 䝛䝑䝖䝽䞊䜽ୖ䛾≀⌮შ䛾⶝ᘏ䛚㔠䛾ὶ㏻ᣑᩓၥ㢟ୡㄽᙧᡂ

䝇䝢䞁ၥ㢟䛂᪂䝛䝑䝖䝽䞊䜽ᛮ⪃ 䞊ୡ⏺䛾䛧䛟䜏䜢ㄞ䜏ゎ䛟䛃䝞䝷䝞䝅 䠄᪥ᮏᨺ㏦ฟ∧༠఍䠅䛂」㞧䛺ୡ⏺䚸༢⣧䛺ἲ๎ 䞊䝛䝑䝖䝽䞊䜽⛉Ꮫ䛾᭱๓⥺䛃䝬䞊䜽䞉䝤䜻䝱䝘䞁 䠄ⲡᛮ♫䠅䛂⚾䛯䛱䛿䛹䛖䛴䛺䛜䛳䛶䛔䜛䛾䛛 䞊䝛䝑䝖䝽䞊䜽䛾⛉Ꮫ䜢ᛂ⏝䛩䜛䛃ቑ⏣┤⣖䠄୰බ᪂᭩䠅䜔䜔ᑓ㛛ⓗ䛂」㞧䝛䝑䝖䝽䞊䜽䛾⛉Ꮫ䛃ቑ⏣┤⣖䚸௒㔝⣖㞝 䠄⏘ᴗᅗ᭩䠅䛂」㞧䝛䝑䝖䝽䞊䜽䠖ᇶ♏䛛䜙ᛂ⏝䜎䛷䛃ቑ⏣┤⣖䚸௒㔝⣖㞝 䠄㏆௦⛉Ꮫ♫䠅ᑓ㛛ⓗ“Characterization of complex networks: A survey of measurements”
L. da F. Costa, F. A. Rodrigues, G. Travieso, and P. R. Villas Boas,Adv. Phys. 56, 167 (2007).
“The structure and function of complex networks”
M. E. J. Newman, SIAM Rev. 45, 167 (2003).
"Evolution of Networks: From Biological Nets to the Internet and WWW”
S. N. Dorogovtsev and J. F. F. Mendes (Oxford Univ Pr., 2003).
“Statistical mechanics of complex networks”
R. Albert and A. L. Barabasi, Rev. Mod. Phys. 74, 47 (2002).
“Evolution of networks”
S. N. Dorogovtsev and J. F. F. Mendes, Adv. Phys. 51, 1079 (2002).

䝺䝫䞊䝖ㄢ㢟䠖୚䛘䜙䜜䛯 N ಶ䛾䝜䞊䝗䛻ᑐ䛧䛶䚸䛣䜜䜙䛾඲䛶䛾䝜䞊䝗ᑐ䜢☜⋡ p 䛷⤖䜆䠄䝸䞁䜽䜢ᙇ䜛䠅䛣䛸䛷ฟ᮶䜛䝛䝑䝖䝽䞊䜽䜢⪃䛘䜛䚹༑ศ኱䛝䛺N䛻䛚䛡䜛䛣䛾䝛䝑䝖䝽䞊䜽䛻ᑐ䛧䛶௨ୗ䛾ၥ䛻⟅䛘䜘䚹(1) ᖹᆒḟᩘ䜢ィ⟬䛫䜘(2) 䜽䝷䝇䝍䞊ಀᩘ䜢ィ⟬䛫䜘(3) ḟᩘศᕸ㛵ᩘ䜢ồ䜑䜘