ᵝ䚻䛺䝛䝑䝖䝽䞊䜽኱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໭ᾏ㐨኱Ꮫ ᕤᏛ◊✲㝔 ᛂ⏝≀⌮Ꮫ㒊㛛▮ஂಖ ⪃௓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౛䠍䠖 ᆅୗ㕲䝛䝑䝖䝽䞊䜽䝛䝑䝖䝽䞊䜽䛸䛿 䠊䠊䠊䝜䞊䝗䝛䝑䝖䝽䞊䜽䝜䞊䝗䠖㥐䝸䞁䜽䠖㊰⥺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౛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౛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౛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౛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
history
MARCELLUS Good now, sit down, and tell me, he that knows, Why this 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, as youknow, by Fortinbras of Norway, Thereto prick'd on by a most emulate
pride, Dared to the combat; inblood
which our valiantman
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⏝䝛䝑䝖䝽䞊䜽䝛䝑䝖䝽䞊䜽䛻㛵䛩䜛⌮ㄽⓗᢅ䛔䠙䝜䞊䝗䠖⺮ⓑ㉁䝸䞁䜽䠖┦஫స⏝䜾䝷䝣⌮ㄽ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」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㉁䖃䝛䝑䝖䝽䞊䜽ᵓ㐀䛻㊥㞳䛾ᴫᛕ䛿䛺䛔ྠ䛨ᵓ㐀䖃㐃⤖ᛶ䛜ኚ䜟䜜䜀ᵓ㐀䛿ኚ䜟䜛␗䛺䜛ᵓ㐀㐃⥆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ከ䛟䛾⌧ᐇ䝛䝑䝖䝽䞊䜽䛻ඹ㏻䛾ᛶ㉁䖃 ⥲䝜䞊䝗ᩘ N䝛䝑䝖䝽䞊䜽䛾䝃䜲䝈䖃 ⥲䝸䞁䜽ᩘ n䖃 䝜䞊䝗䛾ḟᩘ ki
䝜䞊䝗 i 䛛䜙ฟ䛶䛔䜛䝸䞁䜽ᩘ䖃 ᖹᆒḟᩘ <k>k1¦ ki
N i2n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

k N

䖃 䝜䞊䝗㛫㊥㞳 dj䝜䞊䝗ᑐ䜢⤖䜆䝸䞁䜽ᩘ䛾᭱ᑠ್d iji㧗䛔䜽䝷䝇䝍䞊ᛶl v ln N

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ᖹᆒ್䖃 䜽䝷䝇䝍䞊ಀᩘ C

C |0

C |1

䠎䠊䝇䜿䞊䝹䝣䝸䞊ᛶ䝜䞊䝗 i 䛾ḟᩘki

ḟᩘ ki 䛾ศᕸ㛵ᩘ䛜䝧䜻㛵ᩘ䝜䞊䝗 i 䛾㏆᥋䝜䞊䝗ᩘkii㏆᥋䝜䞊䝗䛜஫䛔䛻䝸䞁䜽䛩䜛⤌䜏ྜ䜟䛫䛾ᩘ : Si
Siiki

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
CiEi
Si2 Eiki (ki  1)䝛䝑䝖䝽䞊䜽䛾䜽䝷䝇䝍䞊ಀᩘ 䠖 CC CiC䛿䝛䝑䝖䝽䞊䜽䛜䛹䛾⛬ᗘᐦ䛻⧅䛜䛳䛶䛔䜛䛛䜢⾲䛩㔞᏶඲䜾䝷䝣
C=1䝒䝸䞊ᵓ㐀
C=0(A) ತඃ䛾ඹ₇㛵ಀ䚸(B) WWW䚸(C) 㟁ຊ⥙ㄽᩥ䛾ඹⴭ㛵ಀ䚹(M)ᩘᏛ䚸(NS)⚄⤒⛉Ꮫ䝧䜻ศᕸྵܱƷȍȃȈȯȸǯƷșǭЎࠋP ( k ) v k J䝣䝷䜽䝍䝹ᵓ㐀䛸䝣䝷䜽䝍䝹ḟඖ䠖

(k !! 1)l1

N v l DCl2

䝃䜲䝈 l 䛾⟽䛻ྵ䜎䜜䜛㉁㔞 N 䠄ᗘ䠅ǹǱȸȫȕȪȸࣱ 䠄≉ᚩⓗ䛺k䛜Ꮡᅾ䛧䛺䛔䠅䃒㻩㻞㻚㻝㻌㻌㻌㻌㻔㼃㼃㼃㻕䃒㻩㻞㻚㻠㻌㻌㻌㻌㻔㻵㼚㼠㼑㼞㼚㼑㼠㻕䃒㻩㻞㻚㻝㻌㻌㻌㻌㻔㻺㻿㻕䞉䞉䞉

N B v l B DB
䝃䜲䝈 lB 䛾⟽䛷⿕そ䛩䜛䛾䛻ᚲせ䛺᭱ᑠ䛾⟽䛾ᩘ NBȏȖನᡯᕧ኱䛺䝸䞁䜽ᩘ䜢ᣢ䛴䝜䞊䝗䠄䝝䝤䠅䛜ᑡᩘ䛺䛜䜙Ꮡᅾ䛩䜛lBD 䞉䞉䞉 䝣䝷䜽䝍䝹ḟඖ䠄㠀ᩚᩘ䠅䠏䠊䝣䝷䜽䝍䝹ᛶ㌟䛾ᅇ䜚䛾」㞧䝛䝑䝖䝽䞊䜽䛿䝣䝷䜽䝍䝹䛛䠛ࣇࣛࢡࢱࣝ㸻⮬㌟ࡢ୍㒊ศ࡜┦ఝ࡞ᵓ㐀㸦⮬ᕫ┦ఝ㸧㸻≉ᚩⓗ㛗ࡉࡀ↓࠸ᵓ㐀

N v l DCl v ln N (SW)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 NBN B v l B D䝣䝷䜽䝍䝹⮬↛⏺䛾⮳䜛䛸䛣䜝䛻㐢ᅾlBNB

64

⣽⬊ෆ⏕໬Ꮫ⤒㊰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).

⺮ⓑ㉁┦஫స⏝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䜽䝷䝇䝍䞊ಀᩘp=0䛷䛾䜽䝷䝇䝍䞊ಀᩘከ䛟䛾⌧ᐇ䝛䝑䝖䝽䞊䜽䛻ඹ㏻䛾ᛶ㉁C ( 0)

3( K  2)4( K  1)

䛾䠏ゅᙧ䛜䠏ゅᙧ䛾䜎䜎䛷䛔䜙䜜䜛☜⋡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  p ) 3

C ( p)

඲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ᖹᆒ䝜䞊䝗㛫㊥㞳ఱᨾ䚸䛣䛾䜘䛖䛺ඹ㏻ᛶ䛜Ꮡᅾ䛩䜛䛾䛛䠛f (u )lNf ( pKN )K4tanh 1u 2  4u

3( K  2)(1  p)34( K  1)u

­ const. u  1®
¯ln(u ) / u u !! 1

f (u )

u 2  4u䝇䝰䞊䝹䝽䞊䝹䝗ᛶ䝇䝰䞊䝹䝽䞊䝹䝗ᛶ䛾㉳※

K>>1

Watts-Strogatz 䠄1998䠅
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(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=4
C

p=0

p=134
NKKNln N
ln KCl4( K  1)ḟᩘศᕸ㛵ᩘf (k ,K )P(k )(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

¦
n 0

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㉳※䖃 䝛䝑䝖䝽䞊䜽ᚄBarabasi-Albert 䝰䝕䝹䠄1999䠅

l|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䚹䝷䞁䝎䝮䞉䝛䝑䝖䝽䞊䜽䛸ྠ⛬ᗘ⌧ᐇ䛾䝛䝑䝖䝽䞊䜽䛸୙୍⮴(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 )䠄䝇䝰䞊䝹䝽䞊䝹䝗ᛶ䠛䠅䖃 䜽䝷䝇䝍䞊ಀᩘ(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(ӌm0)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ki¦ kiln Nln ln N

2/6
3/10

3/10
2/6
2/10

i

2/6
2/10

䛷୚䛘䜙䜜䜛䚹䠄ඃඛⓗ㑅ᢥ䠅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㉳※

Barabasi-Albert 䝰䝕䝹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N v l DC

䠄䝣䝷䜽䝍䝹ᛶ䠅l v log N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⮫⏺ⓗ䝇䜿䞊䝹䞉䝣䝸䞊ᛶP ( k ) v k J : J䝝䝤ᵓ㐀

3Song el at. (Nature Phys., 2006)
䝰䞊䝆䝳䞊䝹䛾ධ䜜Ꮚᵓ㐀䝣䝷䜽䝍䝹ᛶ䛾㉳※䛿?䝣䝷䜽䝍䝹ᵓ㐀⮫⏺⌧㇟
ᖹ⾮⣔⮫⏺⌧㇟㠀ᖹ⾮⣔ ⮬ᕫ⤌⧊໬⮫⏺ᛶ (SOC)䖃 Song-Havlin-Makse 䝰䝕䝹䠄2006䠅≉ᚩⓗ㛗䛥䛾↓䛔ᨭ㓄᪉⛬ᘧ

'I 0ᫍᆺ䜾䝷䝣ḟᩘk䛾䝜䞊䝗䛻
mkಶ䛾䝜䞊䝗䜢⧅䛢䜛

1ୡ௦๓䛾䜶䝑䝆䜢䛿䛪䛧ᪧ䝜䞊䝗䛻㞄᥋䛩䜛䝜䞊䝗ྠኈ䜢⧅䛢䜛௙䝣䝷䜽䝍䝹䞉䝛䝑䝖䝽䞊䜽䛾ᙧᡂ䝣䝷䜽䝍䝹ᛶ䛸䝇䜿䞊䝹䝣䝸䞊ᛶ䜢᭷䛩䜛䝰䝕䝹䖃 (u,v)-flower 䝰䝕䝹䠄2007䠅䖃 㐺ᛂᗘ䝰䝕䝹䠄2002, 2010䠅

piji

DP( f ) v f Jfi f jNjfu+vᮏ䛾䜶䝑䝆䛛䜙ᡂ䜛䝃䜲䜽䝹䞉䜾䝷䝣௙ྛ䜶䝑䝆䜢u+vᮏ䛾䜶䝑䝆䛛䜙ᡂ䜛䝃䜲䜽䝹䞉䜾䝷䝣䛻⨨䛝᥮䛘䜛௙」㞧䝛䝑䝖䝽䞊䜽䛾⛉Ꮫ䛾ᒎ㛤䛭䛾௚䛾ၥ㢟䖃 SF䚸SW䚸䝣䝷䜽䝍䝹ᛶ䛾┦஫㛵ಀ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㐀䜢ྲྀ䜛䛛䠛䝇䜿䞊䝹䝣䝸䞊ᛶ䖃 㔜䜏௜䛡䜙䜜䛯䝛䝑䝖䝽䞊䜽䛾ᛶ㉁ྠ᫬ᡂ❧䛩䜛䝰䝕䝹䛿䠛⯟✵㊰⥺䝛䝑䝖䝽䞊䜽ᰴ౯䛾┦㛵䝛䝑䝖䝽䞊䜽⾑⟶⥙䞉䞉䞉䞉䛸D䛻㛵ಀ䛜䛒䜛䛛䝣䝷䜽䝍䝹ᛶ䝇䝰䞊䝹䝽䞊䝹䝗ᛶ䖃 䝛䝑䝖䝽䞊䜽ୖ䛾≀⌮შ䛾⶝ᘏ䛚㔠䛾ὶ㏻ᣑᩓၥ㢟ୡㄽᙧᡂ䝇䝢䞁ၥ㢟䜽䝻䝇䜸䞊䝞䞊ཧ⪃᭩䖃 䝇䜿䞊䝹䝣䝸䞊ᛶ䛸䝇䝰䞊䝹䝽䞊䝹䝗ᛶ▱ே䝰䝕䝹
J. Davidsen et al.: Phys. Rev. Lett. 99, 128701 (2002).

㜈್䝰䝕䝹
呍呍呍

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

୍⯡᭩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♫䠅䖃 䝇䜿䞊䝹䝣䝸䞊ᛶ䛸䝣䝷䜽䝍䝹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DBdkᑓ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ḟ䛾1,2䛾䛖䛱୍䛴䜢㑅䜣䛷ゎ⟅䛫䜘䚹1. 䝷䞁䝎䝮䞉䜾䝷䝣䛾ᖹᆒḟᩘ䚸䜽䝷䝇䝍䞊ಀᩘ䚸䛚䜘䜃ḟᩘศᕸ㛵ᩘ䜢ồ䜑䜘䚹
2. (u,v)-flower䝛䝑䝖䝽䞊䜽䛾䝇䜿䞊䝹䝣䝸䞊ḟᩘ 䛸䝣䝷䜽䝍䝹ḟඖ ௙ 䛜䛭䜜䛮䜜䚸௙䛷୚䛘䜙䜜䜛䛣䛸䜢♧䛫䚹ȩȳȀȠȷǰȩȕ୚䛘䜙䜜䛯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䜛䝛䝑䝖䝽䞊䜽䚹