' $
Islands Vladimir Batagelj Matjazˇ Zaversnikˇ University of Ljubljana
Photo: V. Batagelj, Net
COSIN Meeting at the University of Karlsruhe November 8th and 9th 2004
& version: November 7, 2004 / 22 : 20% V. Batagelj. M. Zaversnik:ˇ Islands
' $ Outline 1 Networks ...... 1 2 Cuts ...... 2 4 Cuts and islands ...... 4 5 Vertex islands ...... 5 10 Simple vertex islands ...... 10 12 Line islands ...... 12 17 Simple line islands ...... 17 19 Example: Reuters Terror News ...... 19 20 Example: US Patents ...... 20 21 Example: The Edinburgh Associative Thesaurus ...... 21 27 Example: Amazon CDs and books networks ...... 27 33 Conclusions ...... 33
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ● ❙ ☛ ✖ & ▲ ▲ ▲ ▲ ▲ ▲ % V. Batagelj. M. Zaversnik:ˇ Islands 1
' Networks $ A network N = (V, L, P, W) consists of:
E.Arkin • a graph G = (V, L), where V J.Mitchell I.Tollis A.Garg M.Bern L.Vismara D.Eppstein
G.diBattista M.Goodrich R.Tamassia is the set of vertices and L =
G.Liotta D.Dobkin S.Suri J.O'Rourke J.Vitter E ∪ A is the set of lines (links, J.Hershberger
B.Chazelle F.Preparata B.Aronov R.Seidel L.Guibas J.Snoeyink ties). Undirected lines E are H.Edelsbrunner M.Sharir P.Agarwal R.Pollack J.Pach D.Halperin P.Gupta called edges, and directed lines M.Smid E.Welzl R.Janardan M.Overmars P.Bose J.Boissonnat M.vanKreveld O.Devillers J.Matousek J.Majhi M.Yvinec C.Yap M.deBerg A are called arcs. J.Schwerdt O.Schwarzkopf G.Toussaint M.Teillaud n = card(V), m = card(L)
J.Czyzowicz J.Urrutia • P vertex value functions / C.Icking R.Klein properties: p : V → A • W line value functions / weights: w : L → B
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
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' Cuts $ • The vertex-cut of a network N = (V, L, p), p : V → IR, at selected level t is a subnetwork N (t) = (V0, L(V0), p), determined by V0 = {v ∈ V : p(v) ≥ t}
and L(V0) is the set of lines from L that have both endpoints in V0. • The line-cut of a network N = (V, L, w), w : L → IR, at selected level t is a subnetwork N (t) = (V(L0), L0, w), determined by L0 = {e ∈ L : w(e) ≥ t}
and V(L0) is the set of all endpoints of the lines from L0. • The line-cut at level t is a vertex-cut at the same level for p(v) = max w(v, u) u∈N(v) where we preserve only lines with w(e) ≥ t.
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ● ❙ ☛ ✖ & ▲ ▲ ▲ ▲ ▲ ▲ % V. Batagelj. M. Zaversnik:ˇ Islands 3
' $
Simple analysis using cuts • After making a cut at selected level t we look at the components of the N (t). Their number and sizes depend on t. Usually there are many small and some large components. Often we consider only components of size at least k and not exceeding K. The components of size smaller than k are discarded as noninteresting, and the components of size larger than K are cut again at some higher level.
• The values of thresholds t, k and K are determined by inspecting the distribution of vertex/line values and the distribution of component sizes and considering additional knowledge about the nature of network or goals of analysis.
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' $
Cuts and islands
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
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' $ Vertex islands • Nonempty subset of vertices C ⊆ V is a vertex island, if – the corresponding induced subgraph G|C = (C, L(C)) is connected, and – the values of the vertices in the neighborhood of C are less than or equal to the values of vertices from C.
max p(u) ≤ min p(v) u∈N(C) v∈C
• Vertex island C ⊆ V is a regular vertex island, if the stronger condition holds: max p(u) < min p(v) u∈N(C) v∈C
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
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' $
Some properties of vertex islands • The sets of vertices of connected components of vertex-cut at selected level t are regular vertex islands.
• The set Hp(N ) of all regular vertex islands of network N is a complete hierarchy: – two islands are disjoint or one of them is a subset of the other – each vertex belongs to at least one island
• Vertex islands are invariant for the strictly increasing transformations of the property p.
• Two linked vertices cannot belong to two disjoint regular vertex islands.
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
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' $
Algorithm for determining maximal regular vertex islands of limited size • We sink the network into the water, then we lower the water level step by step.
• Each time a new vertex v appears from the water, we check with which of the already visible islands is connected.
• We join these islands and the vertex v obtaining a new (larger) island. These islands are subislands of the new island. Vertex v is a port of the new island (the vertex with the smallest value).
• This can be done in O(max(n log n, m)) time.
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ● ❙ ☛ ✖ & ▲ ▲ ▲ ▲ ▲ ▲ % V. Batagelj. M. Zaversnik:ˇ Islands 8
' $
algorithm: hierarchy of islands ...
islands := ∅ sort V in decreasing order according to p for each v ∈ V (in the obtained order) do begin island := new Island() island.port := v island.subislands := {i ∈ islands : i ∩ N(v) 6= ∅} islands := islands ∪ {island}\ island.subislands for each i ∈ island.subislands do i.regular := p(i.port) > p(v) determine the type of island end for each i ∈ islands do i.regular := true
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
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' $
... algorithm: list of islands
L := ∅ while islands 6= ∅ do begin select island ∈ islands islands := islands \{island} if |island| < min then delete island else if |island| > max ∨ ¬island.regular then begin islands := islands ∪ island.subislands delete island end else L := L ∪ {island} end
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
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' $ Simple vertex islands • The set of vertices C ⊆ V is a local vertex peak, if it is a regular vertex island and all of its vertices have the same value.
• Vertex island with a single local vertex peak is called a simple vertex island.
• The types of vertex islands:
– FLAT – all vertices have the same value
– SINGLE – island has a single local vertex peak
– MULTI – island has more than one local vertex peaks
• Only the islands of type FLAT or SINGLE are simple islands.
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ● ❙ ☛ ✖ & ▲ ▲ ▲ ▲ ▲ ▲ % V. Batagelj. M. Zaversnik:ˇ Islands 11
' $ Determining the type of vertex island
if |island.subislands| = 0 then island.type := FLAT else if |island.subislands| = 1 then begin select i ∈ island.subislands if i.type 6= FLAT then island.type := i.type else if p(i.port) = p(v) then island.type := FLAT else island.type := SINGLE end else begin for each i ∈ island.subislands do begin ok := i.type = FLAT ∧ p(i.port) = p(v) if ¬ok then break end if ok then island.type := FLAT else island.type := MULTI end
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
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' $ Line islands • The set of vertices C ⊆ V is a line island, if it is a singleton (degenerated island) or there exists a spanning tree T on C such that the values of lines with exactly one endpoint in C are less than or equal to the values of lines of the tree T .
max w((u ; v)) ≤ min w(e) (u ; v)∈L: e∈L(T ) u∈C∧v6∈C
• Line island C ⊆ V is a regular line island, if the stronger condition holds: max w((u ; v)) < min w(e) (u ; v)∈L: e∈L(T ) u∈C∧v6∈C
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' $
Some properties of line islands • The sets of vertices of connected components of line-cut at selected level t are regular line islands.
• The set Hw(N ) of all nondegenerated regular line islands of network N is hierarchy (not necessarily complete): – two islands are disjoint or one of them is a subset of the other
• Line islands are invariant for the strictly increasing transformations of the weight w.
• Two linked vertices may belong to two disjoint regular line islands.
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
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' $ Algorithm for determining maximal regular line islands of limited size • We sink the network into the water, then we lower the water level step by step.
• Each time a new line e appears from the water, we check with which of the already visible islands is connected (there are exactly two such islands).
• We join these two islands obtaining a new (larger) island. These islands are subislands of the new island. Line e is a port of the new island (not necessarily the line with the smallest value).
• This can be done in O(m log n) time.
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' algorithm: hierarchy of islands ... $
islands := {{v} : v ∈ V} for each i ∈ islands do i.port := null sort L in decreasing order according to w for each e(u ; v) ∈ L (in the obtained order) do begin i1 := island ∈ islands : u ∈ island i2 := island ∈ islands : v ∈ island if i1 6= i2 then begin island := new Island() island.port := e island.subisland1 := i1 island.subisland2 := i2 islands := islands ∪ {island}\{i1, i2} i1.regular := i1.port = null ∨ w(i1.port) > w(e) i2.regular := i2.port = null ∨ w(i2.port) > w(e) end determine the type of island end for each i ∈ islands do i.regular := true
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' $
... algorithm: list of islands
L := ∅ while islands 6= ∅ do begin select island ∈ subislands subislands := subislands \{island} if |island| < min then delete island else if |island| > max ∨ ¬island.regular then begin islands := islands ∪ {island.subisland1, island.subisland2} delete island end else L := L ∪ {island} end
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
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' $ Simple line islands • The set of vertices C ⊆ V is a local line peak, if it is a regular line island and there exists a spanning tree of the corresponding induced network, in which all lines have the same value as the line with the largest value.
• Line island with a single local line peak is called a simple line island.
• The types of line islands:
– FLAT – there exists a spanning tree, in which all lines have the same value as the line with the largest value.
– SINGLE – island has a single local line peak.
– MULTI – island has more than one local line peaks.
• Only the islands of type FLAT or SINGLE are simple islands.
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' $
Determining the type of line islands
p1 := i1.type = FLAT ∧ (i1.port = null ∨ w(i1.port) = w(e)) p2 := i2.type = FLAT ∧ (i2.port = null ∨ w(i2.port) = w(e))
if p1 ∧ p2 then island.type := FLAT else if p1 ∨ p2 then island.type := SINGLE else island.type := MULTI
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ● ❙ ☛ ✖ & ▲ ▲ ▲ ▲ ▲ ▲ % V. Batagelj. M. Zaversnik:ˇ Islands 19
' Example: Reuters Terror News $
airline united_airlines plant
american_airlines attendant Using CRA S. Corman nuclear pakistani herald flight pilot power train and K. Dooley produced arabic-language organization boston weapon manual saudi congressional the Reuters terror news contain service newspaper car passenger member chemical bin_laden network that is based on saudi-born leader rental uniform
inhale necessary all stories released dur- scare dissident taliban suspect firefighter jet fbi call afghanistan airport police knife-wielding agent ing 66 consecutive days by man anthrax world force skin thursday commercial pakistan phone case official airliner officer hijacker special the news agency Reuters arab support terrorism war cell trace hijack country united_states embassy concerning the September jonn deadly business help mighty plane wednesday twin week space strike east 11 attack on the US. The plea attack act military specialist 110-story edmund world_trade_ctr headquarters pentagon terrorist the_worst apparent action vertices of a network are air cheyenne north tower washington morning africa louisiana tuesday south anti-american words (terms); there is an news late terror wyoming city base offutt florida new_york group responsibility air_force mayor edge between two words pfc conference american mayor_giuliani nebraska barksdale team landmark exchange debris iff they appear in the same miss people
dept stock effort text unit. The weight of an rescue thousand market center edward aid buildng fire financial toll edge is its frequency. It has worker smoke plaugher large
postal emergency n = 13332 vertices and chief district death state m = 243447 edges.
Pajek COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
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' $ Example: US Patents
4456712 The citation network of US patents from 5555116 1963 to 1999 (http://www.nber.org/ 5124824 5171469 5283677 patents/) is an example of very large net- 5016988 5122295 5016989
4957349 4877547 4820839 4832462 work (3774768 vertices and 16522438 arcs) that,
4770503 4795579 4797228 4752414 4721367 using some special options in Pajek, can still 4709030 4719032 4695131 4710315 4713197 4704227 4657695 be analyzed on PC with at least 1 G memory. 4630896 4659502 4621901 The islands algorithm was applied on Hummon- 4583826 4510069 4558151 4550981
4526704 4502974 4514044 Doreian SPC weights. 4460770 4480117 4472293 4472592 4455443 The obtained main island is presented in the 4419263 4422951 figure. The vertices represent patents, the size of 4415470 4400293 4386007
4349452 4368135 4340498 a line is proportional to its weight. Collecting
4387039 4387038 4293434 4290905 4361494 4302352 4330426 4357078 from the United States Patent and Trademark 4195916 4229315 4261652 Office (http://patft.uspto.gov/ 4202791 4149413 4198130 netahtml/srchnum.htm) the basic data 4154697 4113647 4130502 4032470 4083797 4082428 4118335
4013582 4029595 4077260 4017416 3975286 4011173 4000084 about the patents we can see that they deal with 3954653 3947375 3960752 3876286 the ’liquid crystal displays’.
3891307 3697150 3636168 3767289 3666948 3322485 3773747 3796479 3795436 2682562 3691755
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' $ Example: The Edinburgh Associative Thesaurus • The Edinburgh Associative Thesaurus is a set of words and the counts of word associations as collected from subjects.
• The data were collected by asking several people to say a word which first comes to their mind upon receiving the stimulus word.
• The network contains 23219 vertices (words) and 325624 arcs (stimulus→response), including 564 loops. Almost 70% of arcs have value 1.
• The subjects were mostly undergraduates from a wide variety of British universities. The age range of the subjects was from 17 to 22 with a mode of 19. The sex distribution was 64 per cent male and 36 per cent female. The data were collected between June 1968 and May 1971.
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' $ Transitivity weight • We would like to identify the most important themes – groups of words with the strongest ties.
• For each arc we determined its weight by counting, to how many transitive triangles it belongs (we are also interested in indirect ties).
• There are 53 line islands of size at least 5 and at most 30. They contain 664 vertices (all together).
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' Selected themes in EAT $
EXPANSE CHAMPIONSHIP WIDE PLAYING
VAST FIVES TEAM
SCOPE
SOCCER GAME BADMINTON TENNIS LARGE SWELL FOOTBALL SPORT RUGGER HUGE GOALIE SPACIOUS
PLAYER NETBALL GAMES BALL BIG RUGBY SIZE ENORMOUS REFEREE HOCKEY BASKETBALL BALLS
SHORTS MASSIVE GYM
DANCE VOICES BICYCLE SONGS BIKE LORRIES SINGING MOTOR CYCLE FESTIVAL POP GROUP DRIVERS SOUNDS SING ROADS
MUSICAL BOX TUNE BICYCLES BIKES SONG TRUCK
RECORDS TONE MUSIC CAR COACH MACHINES MONOTONE RAILWAYS SONATA JAZZ ORCHESTRA LANE VAN STREET PIANO TRAIN RECITAL TRUMPET VIOLIN MUSICIAN MOBILE ROAD CONCERTO MOVING RAILWAY
BEETHOVEN STOPPING SAXOPHONE BACH
STOP PATH
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
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' Selected themes in EAT $
COUCHES PILLOW-CASE DISTRAUGHT DESPAIR ARM-CHAIR SLEEPING BAG COZY MISFORTUNE UNHAPPINESS DISAPPOINTMENT COMFORTABLE BEDDING COSINESS CUSHION GRIEF SLUMBERS COMFORT MISERY SADNESS COUCH SLEEP MATTRESS SORROW BED DEPRESSED SAD UNCOMFORTABLE RELAXED MOOD HAPPY JOY TIREDNESS RELAX DRESSING-GOWN JOYFUL HAPPINESS RELAXING RESTING LAUGHTER RELAXATION SLEEPING CONTENTMENT TIRED LOUNGING TIRING ASLEEP
ENJOYMENT LAUGH BREATHLESS MERRIMENT
PAINS HURT PERCEIVE OBSERVE ILLS INFLICTION
CURE ILL PAIN SICKLY ANGUISH SEE SICK PAINFUL SUFFERING DISEASE WORRY ILLNESS EYES FORESEE DEATH PERCEPTION DESPERATION DIE FEARED
FEAR TERROR DOOM DEAD INSIGHT AFRAID LETHAL SEEING SIGHT DIED
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
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' Selected themes in EAT $
CLOTHS GARMENT AMERICA
REFUGE COUNTRY COSTUME CLOTHES FASHIONED CLOTHE PLACE FARMS SHELTER SUIT COAT DRESS HOME SENT
GARMENTS ARRIVE
CLOTHING SMOCK HOMELY
FROM HOME RETURN LEAVE
BUBBLING BATHROOM SPIRITS STREAM DROWN LIQUID LIQUOR DRUNK RIVERS BATH WHISKY KEG BITTER SINK RIVER ABSORPTION PONDS BEER
WHISKEY BRANDY WATERS LAKES POND WATER SEASIDE GIN SEA DRINK LAKE BOATS SEAS OCEAN BEER-MUG SIPPING BOAT DRIFTING
FLOATING DRY MARTINI SHIP SIP BREAKWATER
SEASCAPE SHIPS LEMONADE LEAKY LAGOON
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
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' Selected themes in EAT $
HAPPEN JUST PAYMENT RECEIPT STOLE YET PAID NOTWITHSTANDING MONIES UNPAID PAY AGAIN ALREADY COINS THRIFTY MONEY INCREASE DEALER HAPPENED LOOT NEVERTHELESS NOW DEFICIT THRIFT PROPERTY MORE MONEY OFTEN BELIEVE OFFER PROVIDE BUT REPAY WHY NO PLEASE AS SOON NOT REFUSE ANYWAY THEREFORE PROBABLY
MEANWHILE SOMETIME COULD
POWERFUL
INHUMAN BOSS
STUDYING LECTURER CHAIRMAN RESPONSIBLE TEACHER ELEGANCE PROFESSION MAN TEACHING HAIRY ENGINEERING
SCHOOL LEARNING MYSTERIOUS NICE EDUCATION CHARM BELOVED
HOMEWORK WORK
ATTRACTIVE TRAINING LOVE GIRL LECTURES DELIGHTFUL SCIENCE LESSONS FLIRT MATHS SCIENTIFIC STUDY KINDNESS BEAUTIFUL LOVELY RESEARCH ADORABLE
ACTIVITY SHAPELY
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
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'Example: Amazon CDs and books networks $ The vertices in Amazon networks are books / CDs; while the arcs are Amazon.com: Books: The Da Vinci Code (Random House Large Print) [LARGE PRI... Page 1 of 7 determined based on the list of products (CDs/books) under the title:
Customers who bought this CD/book also bought BROW SE CORPORATE E-BOOKS NEW & USED USED SEARCH BESTSELLERS MAGAZINES SUBJECTS ACCOUNTS & DOCS TEXTBOOKS BOOKS
SEARCH The Da Vinci Code (Random House Large Print) [LARGE PRINT] Books by DAN BROWN Quantity: 1
List Price: $26.95 Price: $26.95 & This item ships for Sign in to turn on 1-Click ordering. FREE with Super Saver Shipping. See details. 57 used & new from $9.95 Availability: Usually ships within 24 hours Have one to sell? BOOK INFORMATION buying info 57 used & new from editorial reviews Search inside another edition of this book $9.95 customer reviews The Five People You Meet in Heaven Don't have one? search inside Edition: Hardcover We'll set one up for you. by Mitch Albom reading group Other Editions: List Price:Our Price:Other Offers:
guide Hardcover (1st $24.95 $14.97 305 used & new ed) from $5.49 Audio Cassette $25.95 $18.16 57 used & new RECENTLY VIEW ED (Abridged) from $12.00 Digital Fortress: A Triller Audio Cassette $39.95 $27.17 48 used & new The Name of the (Unabridged) from $22.95 by Dan Brown Rose: including See all 9 editions... Life of Pi: A Novel Postscript to the Name of the by Yann Martel Rose by Umberto See more product details Eco (Rate it) All My Hits - Better Together Todos Mis Exitos The Da Vinci Code ~ Selena (Rate it) Buy this book with Angels & Demons by Dan Brown today! Dreaming of You Buy Together Today: $32.54 by Dan Brown ~ Selena (Rate it) Selena - Greatest Hits ~ Selena (Rate it) The Secret Life of Bees See more in the Customers who bought this book also bought: Deception Point Page You Made by Sue Monk Kidd ò The Five People You Meet in Heaven by Mitch Albom (Rate it) by Dan Brown Featured Item: ò Life of Pi by Yann Martel (Rate it) ò Deception Point by Dan Brown (Rate it) ò The Secret Life of Bees by Sue Monk Kidd (Rate it) ò Digital Fortress : A Thriller by Dan Brown (Rate it)
Selena ~ Various Explore Similar Items: 19 in Books, 20 in Music, and 20 in DVD Artists
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ò Hardcover: 752 pages ; Dimensions (in inches): 1.51 x 9.58 x 6.42
http://www.amazon.com/exec/obidos/tg/detail/-/0375432302/qid=1095460140/sr=1-7/r... 18.9.2004
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Amazon.com: Music: All My Hits - Todos Mis Exitos Page 1 of 6 ' $
. . . Amazon CDs and books networks
SEARCH BROW SE TOP NEW & FUTURE FREE ESSENTIAL USED CLASSICAL MUSIC STYLES SELLERS RELEASES DOWNLOADS CDS MUSIC Using relatively simple program written in SEARCH All My Hits - Todos Mis Exitos Selena Popular Music 13 used & new from $4.99 Python we ’harvested’ the books network from
Availability: Usually ships in 1-2 business Have one to sell? days June 16 till June 27, 2004; and the CDs net-
13 used & new from $4.99 work from July 7 till July 23, 2004. Don't have one? See more We'll set one up for you. MUSIC INFORMATION see larger picture product details We harvested only the portion of each network Explore this album buying info listen to samples Customers who bought this title also bought: reachable from the selected starting book/CD. editorial reviews ò All My Hits - Todos Mis Exitos, Vol. 2 [LIMITED EDITION] ~ Selena customer reviews ò Mis Mejores Canciones: 17 Super Exitos ~ Selena (Rate it) The books network has 216737 vertices and RECENTLY VIEW ED Customers who viewed this album also viewed: Dreaming of You ~ Selena (Rate it) 982296 arcs. Selena - Greatest ò Selena - Greatest Hits ~ Selena (Rate it) Hits ~ Selena ò Exitos Y Recuerdos ~ Selena (Rate it) ò Anthology ~ Selena (Rate it) (Rate it) The CDs network has 79244 vertices and ò Ones (CD & DVD) (Limited Edition Package) ~ Selena (Rate it) Selena DVD ~ ò Selena - Greatest Hits (Bonus DVD) ~ Selena (Rate it) Jennifer Lopez ò Momentos Intimos ~ Selena (Rate it) (Rate it) ò Live, The Last Concert - - February 26, 1995, Houston TX ~ Selena 526271 arcs. Crazy Baby ~ (Rate it) Jimmy Smith (Rate it) Explore Similar Items: 9 in Music, 5 in DVD, and 1 in Books By the construction both networks have lim- See more in the Page You Made Product Details ited out-degree and are weakly connected.
Featured Item: ò Essential recordings: Selena ò Audio CD (March 9, 1999) ò Original Release Date: March 9, 1999 178281 books have the out-degree 5; and ò Number of Discs: 1 ò Label: Emi International ò Catalog: #97886 Selena ~ Various ò ASIN: B00000I7XB 55373 CDs have out-degree 8. Artists ò Average Customer Review: Based on 48 reviews. Write a review. RATE THIS ALBUM ò Amazon.com Sales Rank: 8,528 The networks were analysed by Natasaˇ Kejzarˇ (Sign in to rate this item.) ˇ W hat's Your Advice? and Simona Korenjak-Cerne. Visit the DVD Store Is there an item you'd recommend instead of or in addition to this one? Let the world know! Enter the item's ASIN (what's an ASIN?) in the box below, select advice type, then click Submit.
http://www.amazon.com/exec/obidos/tg/detail/-/B00000I7XB/ref=m_art_li_10/002-76... 18.9.2004
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
▲ ▲ ▲ ● ▲ ▲ ▲ ☛ ✖ & % V. Batagelj. M. Zaversnik:ˇ Islands 29
' $
Simple arc islands size distribution We took the number of cyclic triangles as weights on arcs.
Books’ network − islands distribution CDs’ network − islands distribution frequency frequency 1 5 10 50 500 5000 1 5 10 50 100 500
5 10 15 20 25 5 10 15 20 25 30
size of island size of island
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ● ❙ ☛ ✖ & ▲ ▲ ▲ ▲ ▲ ▲ % V. Batagelj. M. Zaversnik:ˇ Islands 30
' Islands with at least 25 vertices $
.NET programming, programming in C#
Catherine Cookson novels
near death experience
pearls
all gems
making jewelery
after death, across the unknown
Pajek COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ● ❙ ☛ ✖ & ▲ ▲ ▲ ▲ ▲ ▲ % V. Batagelj. M. Zaversnik:ˇ Islands 31
' Island of Catherine Cookson novels $
C.Cookson - The Golden Straw C.Cookson - Obsession C.Cookson - The Blind Miller C.Cookson - The Dwelling Place C.Cookson - The Garment & Slinky Jane: Two Wonderful Novels in One Volume
C.Cookson - The Round Tower C.Cookson - Lady on My Left C.Cookson - Silent Lady C.Cookson, D. Yallop - My Beloved Son C.Cookson - Heritage of Folly & The Fen Tiger C.Cookson - Ruthless Need C.Cookson - Feathers in the Fire C.Cookson - The Solace of Sin
C.Cookson, Donnelly - Pure as the Lily
C.Cookson - Rooney & the Nice Bloke: Two Wonderful Novels in One Volume C.Cookson - The Girl C.Cookson - The Fifteen Streets: A Novel C.Cookson - Fanny McBride C.Cookson - The Cultured Handmaiden C.Cookson - Bondage of Love C.Cookson - K. Mulholland C.Cookson - Tilly Trotter: An Omnibus C.Cookson - The Harrogate Secret C.Cookson - Tinker's Girl C.Cookson, W.J. Burley - The Rag Nymph
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ● ❙ ☛ ✖ & ▲ ▲ ▲ ▲ ▲ ▲ %
Pajek V. Batagelj. M. Zaversnik:ˇ Islands 32
' Island of precious stones $
A.L.Matlins - The Pearl Book: The Definitive Buying Guide How to Select, Buy, Care for & Enjoy Pearls G.F.Kunz, C.H.Stevenson - The Book of the Pearl: The History, Art, Science and Industry
R.Newman - Pearl Buying Guide: How to Evaluate, Identify and Select Pearls & Pearl Jewelry N.H.Landman, et al - Pearls: A Natural History R.Newman - Pearl Buying Guide (Gem and Jewelry Buying Guides)
A.Forsyth, et al - Jades from China F.Ward - Pearls F.Ward - Rubies & Sapphires (Fred Ward Gem Book Series)
F.Ward, C.Ward - Diamonds, Third Edition F.Ward - Jade
F.Ward, C.Ward - Emeralds (Fred Ward Gem Books)
R.Keverne - Jade F.Ward, C.Ward - Gem Care FWard, C.Ward - Opals J.Rawson, et al - PB.Downing - Opal Adventures (Rocks, Minerals and Gemstones) Chinese Jade from the Neolithic to the Qing L.Zara - Jade
P.B.Downing - Opal Identification & Value
C.Scott-Clark, A.Levy - The Stone of Heaven: P.B.Downing - Opal Cutting Made Easy (Jewelry Crafts) Unearthing the Secret History of Imperial Green Jade E.J.Soukup - Facet Cutters Handbook (Gembooks) P.B.Downing - Opal: Advanced Cutting & Setting P.D.Kraus - Introduction to Lapidary (Jewelry Crafts)
G.Vargas, M.Vargas - Faceting for Amateurs J.R.Cox - Cabochon Cutting (Gembooks)
J.R.Cox - A Gem Cutter's Handbook: Advanced Cabochon Cutting
H.C.Dake - The Art of Gem Cutting: Including Cabochons Faceting, Spheres, Tumbling, and Special Techniques (Gembooks)
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ● ❙ ☛ ✖ & ▲ ▲ ▲ ▲ ▲ ▲ %
Pajek V. Batagelj. M. Zaversnik:ˇ Islands 33
' Conclusions $ • We proposed an approach to the analysis of networks that can be used also for very large networks with millions of vertices and lines.
• The proposed approach is very general – it can be applied to any property of vertices (vertex islands) and to any weight on lines (line islands).
• The islands algorithms are implemented in Pajek – a program (for Windows) for large network analysis and visualization http://vlado.fmf.uni-lj.si/pub/networks/pajek/ They are available also as a separate program at http://vlado.fmf.uni-lj.si/pub/networks/
• The last version of these slides is available at
http://vlado.fmf.uni-lj.si/pub/networks/doc/mix/islands.pdf
COSIN meeting, November 8th and 9th, 2004, Karlsruhe ❙ ❙
▲ ▲ ▲ ● ▲ ▲ ▲ ☛ ✖ & %