Network workshopVincent Danos, Matthias Hennig, Michael Herrmann (Informatics)
goals of today’s network: - gauging the local college and UoE interest for networks and network-related research- getting interested people to know each other (ie to network :));
see also Dec 16 modelling workshop (organiser: Jane Hillston)
resources: edimod.org.uk, MAN M.Sc. class
socio, techno, eco, bio- things happening on - structured by a network
lots of situations spontaneously organise as networks
- social networks: friendship, acquaintance, co-affiliation, etc, online or not- ecological networks- web pages- citation networks- financial and economical markets
- intra-organisational communication (eg Enron’s emails) - Internet physical structure- power grids
- neural systems- epidemics- intra-celullar networks, etc.
inventory ...
104 | FEBRUARY 2004 | VOLUME 5 www.nature.com/reviews/genetics
R E V I EW S
mathematical properties of random networks14. Theirmuch-investigated random network model assumes thata fixed number of nodes are connected randomly to eachother (BOX 2). The most remarkable property of the modelis its ‘democratic’or uniform character, characterizing thedegree, or connectivity (k ; BOX 1), of the individual nodes.Because, in the model, the links are placed randomlyamong the nodes, it is expected that some nodes collectonly a few links whereas others collect many more. In arandom network, the nodes degrees follow a Poissondistribution, which indicates that most nodes haveroughly the same number of links, approximately equalto the network’s average degree, <k> (where <> denotesthe average); nodes that have significantly more or lesslinks than <k> are absent or very rare (BOX 2).
Despite its elegance, a series of recent findings indi-cate that the random network model cannot explainthe topological properties of real networks. The deviations from the random model have several keysignatures, the most striking being the finding that, incontrast to the Poisson degree distribution, for manysocial and technological networks the number of nodeswith a given degree follows a power law. That is, theprobability that a chosen node has exactly k links follows P(k) ~ k –!, where ! is the degree exponent, withits value for most networks being between 2 and 3 (REF. 15). Networks that are characterized by a power-lawdegree distribution are highly non-uniform, most ofthe nodes have only a few links. A few nodes with a verylarge number of links, which are often called hubs, holdthese nodes together. Networks with a power degreedistribution are called scale-free15, a name that is rootedin statistical physics literature. It indicates the absenceof a typical node in the network (one that could beused to characterize the rest of the nodes). This is instrong contrast to random networks, for which thedegree of all nodes is in the vicinity of the averagedegree, which could be considered typical. However,scale-free networks could easily be called scale-rich aswell, as their main feature is the coexistence of nodes ofwidely different degrees (scales), from nodes with oneor two links to major hubs.
Cellular networks are scale-free. An important develop-ment in our understanding of the cellular networkarchitecture was the finding that most networks withinthe cell approximate a scale-free topology. The first evi-dence came from the analysis of metabolism, in whichthe nodes are metabolites and the links representenzyme-catalysed biochemical reactions (FIG. 1).As manyof the reactions are irreversible, metabolic networks aredirected. So, for each metabolite an ‘in’ and an ‘out’degree (BOX 1) can be assigned that denotes the numberof reactions that produce or consume it, respectively.The analysis of the metabolic networks of 43 differentorganisms from all three domains of life (eukaryotes,bacteria, and archaea) indicates that the cellular metabo-lism has a scale-free topology, in which most metabolicsubstrates participate in only one or two reactions, but afew, such as pyruvate or coenzyme A, participate indozens and function as metabolic hubs16,17.
Depending on the nature of the interactions, net-works can be directed or undirected. In directednetworks, the interaction between any two nodes has awell-defined direction, which represents, for example,the direction of material flow from a substrate to aproduct in a metabolic reaction, or the direction ofinformation flow from a transcription factor to the genethat it regulates. In undirected networks, the links donot have an assigned direction. For example, in proteininteraction networks (FIG. 2) a link represents a mutualbinding relationship: if protein A binds to protein B,then protein B also binds to protein A.
Architectural features of cellular networksFrom random to scale-free networks. Probably the mostimportant discovery of network theory was the realiza-tion that despite the remarkable diversity of networksin nature, their architecture is governed by a few simpleprinciples that are common to most networks of majorscientific and technological interest9,10. For decadesgraph theory — the field of mathematics that dealswith the mathematical foundations of networks —modelled complex networks either as regular objects,such as a square or a diamond lattice, or as completelyrandom network13. This approach was rooted in theinfluential work of two mathematicians, Paul Erdös,and Alfréd Rényi, who in 1960 initiated the study of the
Figure 2 | Yeast protein interaction network. A map of protein–protein interactions18 inSaccharomyces cerevisiae, which is based on early yeast two-hybrid measurements23, illustratesthat a few highly connected nodes (which are also known as hubs) hold the network together.The largest cluster, which contains ~78% of all proteins, is shown. The colour of a node indicatesthe phenotypic effect of removing the corresponding protein (red = lethal, green = non-lethal,orange = slow growth, yellow = unknown). Reproduced with permission from REF. 18 ©Macmillan Magazines Ltd.
yeast proteins
neurons - wikipedia
3-methylglutaconicaciduria
Aarskog-Scottsyndrome
ABCDsyndrome
Abetalipoproteinemia
26
Achondrogenesis_Ib
Achondroplasia
Achromatopsia
Acquiredlong_QT_syndrome
Acromegaly
Adenocarcinoma
Adenoma,periampullary
Adenomas
Adenosine_deaminasedeficiency
Adrenocorticalcarcinoma
Adult_iphenotype
Afibrinogenemia
Alagillesyndrome
Albinism
Alcoholdependence
Alexanderdisease
Allergicrhinitis
96
Alzheimerdisease
Amyloidneuropathy
Amyloidosis
Amyotrophiclateral
sclerosis
Androgeninsensitivity
Anemia
Angelmansyndrome
Angiofibroma,sporadic
117
Aniridia,type_II
Anorexianervosa
126
129
Aorticaneurysm
Apertsyndrome
Apolipoproteindeficiency
137
Aquaporin-1deficiency
144
Arthropathy
Aspergersyndrome
Asthma
Ataxia
Ataxia-telangiectasia
Atelosteogenesis
Atherosclerosis
Atopy
Atrialfibrillation
Atrioventricularblock
Autism
Autoimmunedisease
Axenfeldanomaly
182
Bare_lymphocytesyndrome
Barthsyndrome
Bart-Pumphreysyndrome
Basal_cellcarcinoma
192
Beckermusculardystrophy
Benzenetoxicity
198
Birt-Hogg-Dubesyndrome
Bladdercancer
Bloodgroup
217
Bothniaretinal
dystrophy
Branchiooticsyndrome
Breastcancer
Brugadasyndrome
Butterflydystrophy,
retinal
Complement_componentdeficiency
Cafe-au-laitspots
Caffeydisease
Cancersusceptibility
Capillarymalformations
Carcinoidtumors,
intestinal
Cardiomyopathy
Carneycomplex
275
Cataract
287
Cerebellarataxia
Cerebralamyloid
angiopathy
Cervicalcarcinoma
Charcot-Marie-Toothdisease
Cleftpalate
Coatsdisease
Coffin-Lowrysyndrome
Coloboma,ocular
Coloncancer
347
Conedystrophy
Convulsions
Cornealdystrophy
Coronaryartery
disease
Costellosyndrome
Coumarinresistance
Cowdendisease
CPTdeficiency,
hepatic
Cramps,potassium-aggravated
377
378
379
Craniosynostosis
Creatinephosphokinase
Creutzfeldt-Jakobdisease
Crouzonsyndrome
Cutislaxa
396
Deafness
Dejerine-Sottasdisease
Dementia
Dentindysplasia,
type_II418
Denys-Drashsyndrome
422
Desmoiddisease
Diabetesmellitus
Diastrophicdysplasia
434
439
441
Duchennemusculardystrophy
Dyserythropoieticanemia
Dysfibrinogenemia463
EBD
Ectodermaldysplasia
Ectopia
Ehlers-Danlossyndrome
Elliptocytosis
474
Emphysema
Endometrialcarcinoma
EnhancedS-cone
syndrome
Enlargedvestibularaqueduct
Epidermolysisbullosa
Epidermolytichyperkeratosis
Epilepsy
Epiphysealdysplasia
Episodicataxia
Epsteinsyndrome
Erythrokeratoderma
Esophagealcancer
Estrogenresistance
Exudativevitreoretinopathy
Eyeanomalies
Factor_xdeficiency
Fanconianemia
Fanconi-Bickelsyndrome
Favism
Fechtnersyndrome
Fovealhypoplasia
549
Frasiersyndrome
558
Fundusalbipunctatus
G6PDdeficiency
Gardnersyndrome
Gastriccancer
Gastrointestinalstromaltumor
Germ_celltumor
Gerstmann-Strausslerdisease
Giant-cellfibroblastoma
Glaucoma
Glioblastoma
594
604
Goiter
GRACILEsyndrome
Graft-versus-hostdisease
Gravesdisease
Growthhormone
HDL_cholesterollevel_QTL
Heartblock
Hemangioblastoma,cerebellar
Hematopoiesis,cyclic
Hemiplegic_migraine,familial
Hemolyticanemia
Hemolytic-uremicsyndrome
Hemorrhagicdiathesis
665
Hepaticadenoma
Hirschsprungdisease
Histiocytoma
HIV
Holoprosencephaly
Homocystinuria
Huntingtondisease
Hypercholanemia
Hypercholesterolemia
Hypereosinophilicsyndrome
Hyperinsulinism
733
Hyperlipoproteinemia
Hyperostosis,endosteal
Hyperparathyroidism
Hyperproinsulinemia
Hyperprolinemia
Hyperproreninemia
Hypertension
Hyperthroidism
Hyperthyroidism
Hypertriglyceridemia
Hypoalphalipoproteinemia
Hypobetalipoproteinemia
Hypocalcemia
Hypocalciurichypercalcemia
Hypoceruloplasminemia
Hypochondroplasia
Hypodontia
Hypofibrinogenemia
Hypoglycemia
Hypokalemicperiodicparalysis
Hypothyroidism
792
Ichthyosiformerythroderma Ichthyosis
IgE_levelsQTL
803
Incontinentiapigmenti
Infantile_spasmsyndrome
809
Insensitivityto_pain
Insomnia
Insulinresistance
Intervertebral_discdisease
Iridogoniodysgenesis
Iris_hypoplasiaand_glaucoma
Jackson-Weisssyndrome
Jensensyndrome
830
833
Kallmannsyndrome
Keratitis
843
Keratoconus
845
847
Kniestdysplasia
Larsonsyndrome
868
Leanness,inherited
Lebercongenital_amaurosis
Leighsyndrome
Leopardsyndrome
Leprechaunism
Leprosy
Leukemia
Lhermitte-Duclossyndrome
Liddlesyndrome
LiFraumenisyndrome
Li-Fraumenisyndrome
Lipodystrophy
Lipoma
Lissencephaly
Listeriamonocytogenes
Loeys-Dietzsyndrome
Long_QTsyndrome
913
Lungcancer
Lymphoma
930
Macrocyticanemia
Macrothrombocytopenia
Maculardegeneration
Maculopathy,bull’s-eye
Malaria
942
Maple_syrup_urinedisease
Marfansyndrome
Marshallsyndrome
MASSsyndrome
Mast_cellleukemia
959
May-Hegglinanomaly
McCune-Albrightsyndrome
Medulloblastoma
Melanoma Memoryimpairment
Menieredisease
Meningioma
Menkesdisease
Mentalretardation
Merkel_cellcarcinoma
Mesangialsclerosis
Mesothelioma
Migraine
1016
Miyoshimyopathy
MODY
Mohr-Tranebjaergsyndrome
Morningglorydisc
anomaly
Muenkesyndrome
Muir-Torresyndrome
Multipleendocrineneoplasia
Musculardystrophy
Myasthenicsyndrome
Myelodysplasticsyndrome
Myelofibrosis,idiopathic
Myelogenousleukemia
Myeloperoxidasedeficiency
Myocardialinfarction
Myoclonicepilepsy
1056
1057
Myopathy
Myotilinopathy
Myotoniacongenita
Myxoma,intracardiac
Nasopharyngealcarcinoma
Nephropathy-hypertension
Nethertonsyndrome
Neuroblastoma
Neuroectodermaltumors
Neurofibromatosis
1096
Neurofibromatosis
Neurofibrosarcoma
Neuropathy
Neutropenia
Nevosyndrome
11041105
Nicotineaddiction
Nightblindness
Nijmegen_breakagesyndrome
1113
Non-Hodgkinlymphoma
Nonsmall_celllung_cancer
Noonansyndrome
Norriedisease
Obesity
Obsessive-compulsivedisorder
Occipital_hornsyndrome
Oculodentodigitaldysplasia
Oligodendroglioma
Oligodontia
1140
Omennsyndrome
Opticatrophy
Orolaryngealcancer
OSMEDsyndrome
Osseousheteroplasia
1153
Osteoarthritis
Osteogenesisimperfecta
Osteopetrosis
Osteoporosis 1164
Osteosarcoma
Ovariancancer
1174
Pancreaticcancer
1183
Paragangliomas
Paramyotoniacongenita
Parathyroidadenoma
Parietalforamina
Parkes_Webersyndrome
Parkinsondisease
Partingtonsyndrome
PCWH
Pelizaeus-Merzbacherdisease
Pendredsyndrome
Perinealhypospadias
Petersanomaly
Peutz-Jegherssyndrome
Pfeiffersyndrome
Pheochromocytoma
Pickdisease
Piebaldism
1229
Pilomatricoma
1232
Placentalabruption
Plateletdefect/deficiency
1239
Polycythemia
Polyposis
PPM-Xsyndrome
Preeclampsia
Primarylateral_sclerosis
1263
1267
Prostatecancer
Proudsyndrome
Pseudoachondroplasia
Pseudohypoaldosteronism
Pseudohypoparathyroidism
Pyropoikilocytosis
1297
Rabson-Mendenhallsyndrome
Renal_cellcarcinoma
Retinal_conedsytrophy
Retinitispigmentosa
Retinoblastoma
Rettsyndrome
Rhabdomyosarcoma
Rheumatoidarthritis
Rh-modsyndrome
Rh-negativeblood_type
Riegersyndrome
Ring_dermoidof_cornea
Rippling_muscledisease
Roussy-Levysyndrome
Rubenstein-Taybisyndrome
Saethre-Chotzensyndrome
Salivaryadenoma
1347
SARS,progression_of
Schizophrenia
Schwannomatosis
Sea-blue_histiocytedisease
Seasonalaffective_disorder
Sebastiansyndrome
Self-healingcollodion_baby
Sepsis
1383
Sezarysyndrome
Shah-Waardenburgsyndrome
Shprintzen-Goldbergsyndrome
Sick_sinussyndrome
1396
Simpson-Golabi-Behmelsyndrome
1401
SMEDStrudwick_type
1414
Somatotrophinoma
Spastic_ataxia/paraplegia
Spherocytosis
Spinal_muscularatrophy
Spinocereballarataxia
1432
Spondyloepiphysealdysplasia
Squamous_cellcarcinoma
Stargardtdisease
Sticklersyndrome
Stomachcancer
Stroke
1456
Supranuclearpalsy
Supravalvar_aorticstenosis
Syndactyly
Systemic_lupuserythematosus
Tangierdisease
1476
T-celllymphoblastic
leukemia
Tetralogyof_Fallot
1490
Thrombocythemia
Thrombocytopenia
Thrombophilia
Thyroidcarcinoma
Thyrotoxicperiodicparalysis
Tietzsyndrome
Toenaildystrophy,
isolated
1518
1528
Turcotsyndrome
1545
Urolithiasise
Ushersyndrome
Uterineleiomyoma
van_Buchemdisease
1555
Ventriculartachycardia
Verticaltalus
Viralinfection
Vitelliformmacular
dystrophy
Vohwinkelsyndrome
von_Hippel-Lindausyndrome
Waardenburg-Shahsyndrome
Waardenburgsyndrome
Wagnersyndrome
WAGRsyndrome
Walker-Warburgsyndrome
Watsonsyndrome
Wegenergranulomatosis
Weill-Marchesanisyndrome
1586
Williams-Beurensyndrome
Wilmstumor
Wiskott-Aldrichsyndrome
Witkopsyndrome
Wolff-Parkinson-Whitesyndrome
1614
Zlotogora-Ogursyndrome
Adrenaladenoma
Adrenal_corticalcarcinoma
Aneurysm,familial_arterial
Autoimmunethyroiddisease
Basal_cellnevus_syndrome
Carcinoid_tumorof_lung
Central_coredisease
Coronaryspasms
2385
2785
Maculardystrophy
Medullary_thyroidcarcinoma
Pancreaticagenesis
3212
3229
Thyroidhormoneresistance
3512
3558
Combinedimmunodeficiency
Multiplemalignancysyndrome
Optic_nervehypoplasia/aplasia
5233
Renaltubularacidosis
Multiplesclerosis
Renaltubular
dysgenesis
ABCA1
ABCA4
ADA
ADRB2
AGRP
JAG1
AGTAGTR1
ALOX5
ALOX5AP
APC
APOA1
APOA2
APOB
APOE
APPFAS
AQP1
AR
STS
ATM
ATP1A2
ATP7A
BAX
CCND1
BCS1L
BDNF
BMPR1A
BRCA1
BRAF
BRCA2
C6
CACNA1A
CACNA1S
CACNB4
CASP8
CASP10
CASR
CAV3
RUNX1
CBS
CD36
CDH1
CDKN2A
CHRNA4
COL1A1
COL1A2
COL2A1
COL3A1
COL7A1
COL8A2
COL9A2
COL9A3
COL11A1
COL11A2
COMP
KLF6
COX15
CP
CPT2
CRX
CRYAB
NKX2-5
CTLA4
CTNNB1
CYP1B1
CYP2A6
DBH
ACE
DCTN1
DCX
DES
TIMM8A
COCH
NQO1
DMDDSP
DSPP
SLC26A2
ECE1
EDN3
EDNRB
EGFR
EGR2
ELA2
ELN
EP300
EPHX1ERBB2
EYA4
ESR1
EYA1
F5
F7
FBN1
FCGR3A
FCMD
FGA
FGB
FGD1
FGFR1
FGFR3
FGFR2
FGG
FOXC1
FLNB
G6PD
GABRG2
GARS
GATA1
GCK
GCNT2
GCSL
GDNF
GJA1
GJB2GJB3
GPC3
GNAI2GNAS
GSS
MSH6
GYPC
GUCY2D
HEXB
CFH
HNF4A
HOXD10
HRAS
HSD11B2
HSPB1
HTR2A
IL2RG
IL10
IL13
INS
INSR
IPF1
IRF1
JAK2
KCNE1
KCNH2
KCNJ11
KCNQ1
KCNQ2
KIT
KRAS
KRT1
KRT10
LAMA3
LMNA
LOR
LPP
LRP5
SMAD4
MAPT
MATN3
MECP2
MEN1
MET
CIITA
MITF
MLH1 NR3C2
MPO
MPZ
MSH2
MSX1
MSX2
MUTYH
MXI1
MYF6MYH6
MYH7
MYH8
MYH9
MYO7A
NBN
NDP
NDUFV1
NDUFS4
NF1
NF2
NOS3
NRL
NTRK1
OPA1
SLC22A18
PAFAH1B1
PARK2
PAX3
PAX6
PAX9
PDGFB
PDGFRA
PDGFRL
PDE6B
PDHA1
ENPP1
SLC26A4
PGK1
SERPINA1
PIK3CA
PITX2 PITX3
PLEC1
PLOD1
PLP1
PMP22
PMS2
PPARG
PRKAR1A
PRNP
PRODH
PSEN1
PTCH
PTEN
PTPN11
PTPRC
PVRL1
RAG1
RAG2
RASA1
RB1
RDS
REN
RET
RHAG
RHCE
RHO
RLBP1
RP1
RPGR
RPE65
RPS6KA3
RYR1
RYR2
SCN4A
SCN5A
SCNN1B
SCNN1G
SDHA
SDHBSDHD
SGCD
SHH
SLC2A2
SLC4A1
SLC6A4
SLC6A8
SLC34A1
SNCA
SOX3
SOX10
SPTA1
SPTB
STAT5B
ELOVL4
STK11
ABCC8
TAP2
TAZ
TBP
TCF1
TCF2
TG
TGFBR2
TGM1
THBD
TNF
TP53
TPO
TSHR
TTN
TTR
TYR
USH2A
VHL
VMD2
WAS
WT1
XRCC3
PLA2G7
HMGA2
DYSF
AXIN2
MAD1L1
RAD54L
IKBKG
TCAP
PTCH2
WISP3
BCL10
PHOX2B
LGI1
VAPB
MYOT
KCNE2
NR2E3
USH1C
FBLN5
POMT1
GJB6
SPINK5
CHEK2
ACSL6
CRB1
AIPL1
RAD54B
PTPN22
BSCL2
VSX1FOXP3
PHF11
PRKAG2
NLGN3
CNGB3
RETN
RPGRIP1
NLGN4X
ALS2
CDH23
DCLRE1C
PCDH15
CDC73
OPA3
BRIP1
MASS1
ARX
FLCN
Abacavirhypersensitivity
18
Acrocallosalsyndrome
Acrocapitofemoraldysplasia
Acrokeratosisverruciformis
Acromesomelicdysplasia
53
Adrenoleukodystrophy
Adrenomyeloneuropathy
ADULTsyndrome
Agammaglobulinemia
AIDS
77
AldosteronismAlopecia
universalis
Alperssyndrome
87
Alpha-actinin-3deficiency
92
Alportsyndrome
Amelogenesisimperfecta
Analbuminemia
107
Andersondisease
Anhaptoglobinemia
Ankylosingspoldylitis
Antley-Bixlersyndrome
Aplasticanemia
Aromatasedeficiency
Arthrogryposis
162
Atransferrinemia
Atrichia w/papular lesions
171
Bardet-Biedlsyndrome
BCGinfection
Beckwith-Wiedemannsyndrome
Bernard-Souliersyndrome
Bethlemmyopathy
Blausyndrome
210
Blepharospasm
Blue-conemonochromacy
Bombayphenotype
Bosley-Salih-Alorainysyndrome
Brachydactyly
Buschke-Ollendorffsyndrome
Calcinosis,tumoral
Campomelicdysplasia
Cartilage-hairhypoplasia
279
292
294Ceroid
lipofuscinosis
Ceroid-lipofuscinosis
CETPdeficiency
Cholelithiasis
Cholestasis
313
Chondrocalcinosis
Chondrosarcoma
Chorea,hereditary
benign
320
Chudley-Lowrysyndrome
329
Chylomicronretentiondisease
Ciliarydyskinesia
CINCAsyndrome
Cleidocranialdysplasia
Cockaynesyndrome
Codeinesensitivity
344
Colorblindness
Congestiveheartfailure
Conjunctivitis,ligneous
357
Coproporphyria
Craniometaphysealdysplasia
CRASHsyndrome
Crigler-Najjarsyndrome
Crohndisease
Cystathioninuria
Cysticfibrosis
CystinuriaDarierdisease
Debrisoquinesensitivity
Dentalanomalies,
isolated
Dentdisease
De Sanctis-Cacchionesyndrome
DiGeorgesyndrome
438
Dosage-sensitivesex
reversal
Double-outletright ventricle
Downsyndrome
452
453
Dyskeratosis
Dysprothrombinemia
461
Dystonia
EEC syndrome
471
Ellis-van Creveldsyndrome
Enchondromatosis
Erythremias
Erythrocytosis
Ewingsarcoma
Exostoses
527
Fertileeunuch
syndrome
535
Fibromatosisl
539
Fish-eyedisease
Fitzgerald factordeficiency
544
545
Frontometaphysealdysplasia
Fumarasedeficiency
Gaucherdisease
584
Gilbertsyndrome
GM-gangliosidosis
Greenbergdysplasia
626
Guttmachersyndrome
Haim-Munksyndrome
Hand-foot-uterussyndrome
Harderoporphyrinuria
HARPsyndrome
Hay-Wellssyndrome
646
Heinzbody
anemia
HELLPsyndrome
Hemangioma
Hematuria,familial_benign
Hemochromatosis
Hemoglobi_Hdisease
Hemophilia
Heterotaxy
Heterotopia
Hex_Apseudodeficiency
679
Homocysteineplasma
level
699 701
Hoyeraal-Hreidarssonsyndrome
HPFH
HPRT-relatedgout
H._pyloriinfection
Hyalinosis,infantilesystemic
Hydrocephalus
Hyperalphalipoproteinemia
Hyperandrogenism
Hyperbilirubinemia
Hyperekplexia
727
Hyper-IgDsyndrome
734
Hypermethioninemia
Hyperphenylalaninemia
Hyperprothrombinemia
Hypertrypsinemia
Hyperuricemicnephropathy
Hypoaldosteronism
Hypochromicmicrocytic
anemia
Hypogonadotropichypogonadism
Hypohaptoglobinemia
Hypolactasia,adulttype
780
Hypophosphatasia
Hypophosphatemia
Hypophosphatemicrickets
785
Hypoprothrombinemia
Inclusionbody
myopathy
Ironoverload/deficiency
Joubertsyndrome
Juberg-Marsidisyndrome
Kanzakidisease
Kartagenersyndrome
Kenny-Caffeysyndrome-1
Kininogendeficiency
Langermesomelicdysplasia
Larondwarfism
LCHADdeficiency
Leadpoisoning
Leiomyomatosis
Leri-Weilldyschondrosteosis
Lesch-Nyhansyndrome,
891
Leydigcell
adenoma
LIG4syndrome
Limb-mammarysyndrome
Lipoproteinlipase
deficiency
Longevity
Lowesyndrome
Low reninhypertension
Lymphangioleiomyomatosis
Lymphedema
945
MASAsyndrome
McKusick-Kaufmansyndrome
969
Melnick-Needlessyndrome
982
Meningococcaldisease
Mephenytoinpoor metabolizer
Metachromaticleukodystrophy
Metaphysealchondrodysplasia
Methemoglobinemia
10011002
Mevalonicaciduria
Microcephaly
Micropenis
Microphthalmia
Muckle-Wellssyndrome
Mucopolysaccharidosis
Mycobacterialinfection
Myelokathexis,isolated
1050
Myeloproliferativedisorder
Nemalinemyopathy
1080
Nephrolithiasis
Nephronophthisis
1090
Neurodegeneration
Nonakamyopathy
Norumdisease
1119
Ocularalbinism
1133
Odontohypophosphatasia
Opremazolepoor metabolizer
Orofacial cleft
Osteolysis
Osteopoikilosis
Otopalatodigitalsyndrome
Ovarioleukodystrophy
Pachyonychiacongenita
Pagetdisease
Pallister-Hallsyndrome
Palmoplantarkeratoderma
Pancreatitis
Papillon-Lefevresyndrome
Pelger-Huetanomaly
Periodontitis
Phenylketonuria
1227 Plasminogendeficiency
1238
Polydactyly
Poplitealpterygiumsyndrome
Porphyria
Precociouspuberty,
male
Prematureovarianfailure
1265
Proguanilpoor metabolizer
Proteinuria
Pseudohermaphroditism,male
Psoraisis
Pulmonaryfibrosis
RAPADILINOsyndrome
Rapp-Hodgkinsyndrome
Red hair/fair skin
Refsumdisease
Restingheartrate
Restrictivedermopathy,
lethal
1325
1335
Rothmund-Thomsonsyndrome
Salladisease
Sarcoidosis
Schindlerdisease
1361
Senior-Lokensyndrome
1376
Septoopticdysplasia
Sexreversal
Shortstature
Sialidosis
Sialuria
Sicklecell
anemia
Situsambiguus
Smith-Fineman-Myerssyndrome
Smith-McCortdysplasia
Sotossyndrome
Spinabifida
Split-hand/footmalformation
Spondylometaphysealdysplasia
1438
Startledisease
STAT1deficiency
Steatocystomamultiplex
1446
Surfactantdeficiency
Sutherland-Haansyndrome-like
1466
Symphalangism,proximal
Synostosessyndrome
Synpolydactyly
Tallstature
1475
Tay-Sachsdisease
Thalassemias
Thymine-uraciluria
Tolbutamidepoor
metabolizer
1519
Trichodontoosseoussyndrome
Trichothiodystrophy
1526
Tropicalcalcific
pancreatitis
Tuberculosis
Tuberoussclerosis
Twinning,dizygotic
1542
UV-inducedskin damage
Velocardiofacialsyndrome
Virilization
1565
1580
Weaversyndrome
Weyersacrodentaldysostosis
WHIMsyndrome
Wolframsyndrome
Wolmandisease
Xerodermapigmentosum
1611
Yellownail
syndrome
Zellwegersyndrome
Adrenocorticalinsufficiency
Chondrodysplasia,Grebetype
2327
Combinedhyperlipemia
2354
Diabetesinsipidus
3037
3144
Ovariandysgenesis
3260van_der_Woude
syndromeBasal
gangliadisease
42915170
Pituitaryhormonedeficiency
Renalhypoplasia,
isolated
Ovariansex cordtumors
CombinedSAP deficiency
Multiplemyeloma
SERPINA3
ACTN3
ADRB1
NR0B1
ALAD
ALB
ABCD1
ALPL
ATP2A2
ATRX
AVPR2
FOXL2
BTK
RUNX2KRIT1
CETP
CTSC
CFTR
CLCN5COL4A4
COL6A1
COL6A2
COL6A3
COL10A1
CPOX
CTH
CYP2C19
CYP2C9
CYP2D6
CYP11B1
CYP11B2
CYP19A1
CYP21A2
DKC1
DLX3
DNAH5
DPYD
DRD5
ERCC2
ERCC3
ERCC5
ERCC6
EVC
EWSR1
EXT1
F2
F9
FH
FOXC2
FLNA
FLT4
FSHR
FTL
NR5A1
FUT2OPN1MW
GHR
GLB1
GLI3
GLRA1
GNRHR
GP1BB
HADHA
HBA1
HBA2
HBB
HEXA
HFE
HLA-B
HOXA1
HOXA13HOXD13
HP
HPRT1
HSPG2
IFNG
IFNGR1
IHHIRF6
KNG1
KRT16
KRT17
L1CAM
LBR
LCAT
LHCGR
LIG4
LIPA
LPL
MAT1A
MBL2
MC1R
MCM6
MTHFD1
MTR MTRR MVK
NAGA
NPHP1
ROR2
OCRL
PAH
PAX2
PDGFRB
PEX1
PEX7
PEX10
PEX13
ABCB4
PLG
POLG
POR
PPT1
PSAPPTHR1
PXMP3
PEX5
OPN1LW
RMRP
SFTPC
SHOX
SLC3A1
SOX9
SPINK1
STAT1
TBX1
TBCE
TERC
TF
TITF1
TPM2
TSC1TSC2
UMOD
WFS1
CXCR4
FGF23
MKKS
GDF5
TP73L
DNAH11
TNFRSF11A
HESX1
EIF2B4
EIF2B2EIF2B5
NOG
RECQL4
GNEENAM
ZMPSTE24
LEMD3
SLC17A5
DNAI1
SAR1B
SLC45A2
UGT1A1
DYM
BCOR
PEX26
HR
CFC1
ANKH
CARD15
NSD1
VKORC1
MCPH1
PANK2
CIAS1
ANTXR2
NPHP4
The human disease networkGoh K-I, Cusick ME, Valle D, Childs B, Vidal M, Barabasi A-L (2007) Proc Natl Acad Sci USA 104:8685-8690!
Supporting Information Figure 13 | Bipartite-graph representation of the diseasome. A disorder (circle) and a gene (rectangle) are connected if the gene is implicated in the disorder. The size of the circle represents the number of distinct genes associated with the disorder. Isolated disorders (disorders having no links to other disorders) are not shown. Also, only genes connecting disorders are shown.
Disorder Class
Disorder Name
BoneCancerCardiovascularConnective tissue disorderDermatologicalDevelopmentalEar, Nose, ThroatEndocrineGastrointestinalHematologicalImmunologicalMetabolicMuscularNeurologicalNutritionalOphthamologicalPsychiatricRenalRespiratorySkeletalmultipleUnclassified
5233 Placental steroid sulfatase deficiency5170 Ovarian hyperstimulation syndrome4291 Cerebral cavernous malformations3558 Ventricular fibrillation, idiopathic3512 Total iodide organification defect3260 Premature chromosome condensation w/ microcephaly, mental retardation3229 Pigmented adrenocortical disease, primary isolated3212 Persistent hyperinsulinemic hypoglycemia of infancy3144 Optic nerve coloboma with renal disease3037 Multiple cutaneous and uterine leiomyomata2785 Hypoplastic left heart syndrome2385 Creatine deficiency syndrome, X-linked2354 Congenital bilateral absence of vas deferens2327 Chronic infections, due to opsonin defect1614 Yemenite deaf-blind hypopigmentation syndrome1611 XLA and isolated growth hormone deficiency1586 Weissenbacher-Zweymuller syndrome1580 Warfarin resistance/sensitivity1565 Vitamin K-dependent coagulation defect1555 VATER association with hydrocephalus1545 Unna-Thost disease, nonepidermolytic1542 Ullrich congenital muscular dystrophy1528 Trismus-pseudocomptodactyly syndrome1526 Trifunctional protein deficiency1519 Transposition of great arteries, dextro-looped1518 Transient bullous of the newborn1490 Thanatophoric dysplasia, types I and II1476 Tauopathy and respiratory failure1475 Tarsal-carpal coalition syndrome1466 Sweat chloride elevation without CF1456 Subcortical laminar heterotopia1446 Stevens-Johnson syndrome, carbamazepine-induced1438 Stapes ankylosis syndrome without symphalangism1432 Spondylocarpotarsal synostosis syndrome1414 Solitary median maxillary central incisor1401 Skin fragility-woolly hair syndrome1396 Silver spastic paraplegia syndrome1383 Severe combined immunodeficiency1376 Sensory ataxic neuropathy, dysarthria, and ophthalmoparesis1361 Schwartz-Jampel syndrome, type 11347 Sandhoff disease, infantile, juvenile, and adult forms1335 Robinow syndrome, autosomal recessive1325 Rhizomelic chondrodysplasia punctata1297 Pyruvate dehydrogenase deficiency1267 Prolactinoma, hyperparathyroidism, carcinoid syndrome1265 Progressive external ophthalmoplegia with mitochondrial DNA deletions1263 Prion disease with protracted course1239 Pneumothorax, primary spontaneous1238 Pneumonitis, desquamative interstitial1232 Pituitary ACTH-secreting adenoma1229 Pigmented paravenous chorioretinal atrophy1227 Pigmentation of hair, skin, and eyes, variation in1183 Papillary serous carcinoma of the peritoneum1174 Pallidopontonigral degeneration1164 Osteoporosis-pseudoglioma syndrome1153 Ossification of the posterior longitudinal spinal ligaments1140 Oligodontia-colorectal cancer syndrome1133 Oculofaciocardiodental syndrome1119 Norwalk virus infection, resistance to1113 Noncompaction of left ventricular myocardium1105 Newfoundland rod-cone dystrophy1104 Nevus, epidermal, epidermolytic hyperkeratotic type1096 Neurofibromatosis-Noonan syndrome1090 Neural tube defects, maternal risk of1080 Nephrogenic syndrome of inappropriate antidiuresis1057 Myokymia with neonatal epilepsy1056 Myoglobinuria/hemolysis due to PGK deficiency1050 Myelomonocytic leukemia, chronic1016 Mitochondrial complex deficiency1002 Methylcobalamin deficiency, cblG type1001 Methionine adenosyltransferase deficiency, autosomal recessive982 Melorheostosis with osteopoikilosis969 Medullary cystic kidney disease959 Mastocytosis with associated hematologic disorder945 Mandibuloacral dysplasia with type B lipodystrophy942 Malignant hyperthermia susceptibility930 Lynch cancer family syndrome II913 Lower motor neuron disease, progressive, without sensory symptoms891 Leukoencephalopathy with vanishing white matter868 Laryngoonychocutaneous syndrome847 Keratosis palmoplantaria striata845 Keratoderma, palmoplantar, with deafness843 Keratitis-ichthyosis-deafness syndrome833 Juvenile polyposis/hereditary hemorrhagic telangiectasia syndrome830 Jervell and Lange-Nielsen syndrome809 Infundibular hypoplasia and hypopituitarism803 Immunodysregulation, polyendocrinopathy, and enteropathy, X-linked792 Hystrix-like ichthyosis with deafness785 Hypoplastic enamel pitting, localized780 Hypoparathyroidism-retardation-dysmorphism syndrome734 Hyperkeratotic cutaneous capillary-venous malformations733 Hyperkalemic periodic paralysis727 Hyperferritinemia-cataract syndrome701 Homozygous 2p16 deletion syndrome699 Homocystinuria-megaloblastic anemia, cbl E type679 High-molecular-weight kininogen deficiency665 Hemosiderosis, systemic, due to aceruloplasminemia646 Hearing loss, low-frequency sensorineural626 Greig cephalopolysyndactyly syndrome604 Glutathione synthetase deficiency594 Glomerulocystic kidney disease, hypoplastic584 Giant platelet disorder, isolated558 Fuchs endothelial corneal dystrophy549 Foveomacular dystrophy, adult-onset, with choroidal neovascularization545 Focal cortical dysplasia, Taylor balloon cell type544 Fluorouracil toxicity, sensitivity to539 Fibular hypoplasia and complex brachydactyly535 Fibrocalculous pancreatic diabetes527 Fatty liver, acute, of pregnancy474 Emery-Dreifuss muscular dystrophy471 Elite sprint athletic performance463 Dystransthyretinemic hyperthyroxinemia461 Dyssegmental dysplasia, Silverman-Handmaker type453 Dysalbuminemic hyperthyroxinemia452 Dyggve-Melchior-Clausen disease441 Dopamine beta-hydroxylase deficiency439 Dissection of cervical arteries438 Disordered steroidogenesis, isolated434 Dilated cardiomyopathy with woolly hair and keratoderma422 Dermatofibrosarcoma protuberans418 Dentinogenesis imperfecta, Shields type396 Cyclic ichthyosis with epidermolytic hyperkeratosis379 Craniofacial-skeletal-dermatologic dysplasia378 Craniofacial-deafness-hand syndrome377 Craniofacial anomalies, empty sella turcica, corneal endothelial changes357 Conotruncal anomaly face syndrome347 Colonic aganglionosis, total, with small bowel involvement344 Cold-induced autoinflammatory syndrome329 Chylomicronemia syndrome, familial320 Choreoathetosis, hypothyroidism, and respiratory distress313 Cholesteryl ester storage disease294 Cerebrovascular disease, occlusive292 Cerebrooculofacioskeletal syndrome287 Central hypoventilation syndrome279 Cavernous malformations of CNS and retina275 Carpal tunnel syndrome, familial217 Bone mineral density variability210 Blepharophimosis, epicanthus inversus, and ptosis198 Beta-2-adrenoreceptor agonist, reduced response to192 Beare-Stevenson cutis gyrata syndrome182 Bannayan-Riley-Ruvalcaba syndrome171 Attention-deficit hyperactivity disorder162 Athabaskan brainstem dysgenesis syndrome144 Arrhythmogenic right ventricular dysplasia137 Apparent mineralocorticoid excess, hypertension due to129 Anxiety-related personality traits126 Anterior segment anomalies and cataract117 Angiotensin I-converting enzyme107 Analgesia from kappa-opioid receptor agonist, female-specific96 Alternating hemiplegia of childhood92 Alpha-thalassemia/mental retardation syndrome87 Alpha-1-antichymotrypsin deficiency77 Aldosterone to renin ratio raised53 Adrenal hyperplasia, congenital26 Achondrogenesis-hypochondrogenesis, type II18 Acampomelic campolelic dysplasia
Vidal, Barabasi, PNAS 2007
diseases and genes
4.1. HOMOPHILY 87
Figure 4.1: Homophily can produce a division of a social network into densely-connected, homogeneous
parts that are weakly connected to each other. In this social network from a town’s middle school and
high school, two such divisions in the network are apparent: one based on race (with students of different
races drawn as differently colored circles), and the other based on friendships in the middle and high schools
respectively [304].
hypothesizing intrinsic mechanisms: when individuals B and C have a common friend A,
then there are increased opportunities and sources of trust on which to base their interactions,
and A will also have incentives to facilitate their friendship. However, social contexts also
provide natural bases for triadic closure: since we know that A-B and A-C friendships
already exist, the principle of homophily suggests that B and C are each likely to be similar
to A in a number of dimensions, and hence quite possibly similar to each other as well. As
a result, based purely on this similarity, there is an elevated chance that a B-C friendship
will form; and this is true even if neither of them is aware that the other one knows A.
The point isn’t that any one basis for triadic closure is the “correct” one. Rather, as we
take into account more and more of the factors that drive the formation of links in a social
high-school friendship
70 CHAPTER 3. STRONG AND WEAK TIES
Figure 3.12: A co-authorship network of physicists and applied mathematicians working onnetworks [322]. Within this professional community, more tightly-knit subgroups are evidentfrom the network structure.
We will refer to this as the problem of graph partitioning, and the constituent parts the
network is broken into as the regions arising from the partitioning method. Formulating a
method for graph partitioning will implicitly require working out a set of definitions for all
these notions that are both mathematically tractable and also useful on real datasets.
To give a sense for what we might hope to achieve from such a method, let’s consider
two examples. The first, shown in Figure 3.12, depicts the co-authorships among a set of
physicists and applied mathematicians working on networks [322]. Recall that we discussed
co-authorship networks in Chapter 2 as a way of encoding the collaborations within a profes-
sional community. It’s clear from the picture that there are tightly-knit groups within this
community, and some people who sit on the boundaries of their respective groups. Indeed it
resembles, at a somewhat larger scale, some of the pictures of tightly-knit groups and weak
ties that we drew in schematic form earlier, in examples such as Figure 3.11. Is there a
general way to pull these groups out of the data, beyond using just our visual intuition?
co-authors
NYT May 1st 2010
euro debt network
the internet
1.1. ASPECTS OF NETWORKS 5
Figure 1.4: The links among Web pages can reveal densely-knit communities and prominentsites. In this case, the network structure of political blogs prior to the 2004 U.S. Presiden-tial election reveals two natural and well-separated clusters [5]. (Image from http://www-personal.umich.edu/ ladamic/img/politicalblogs.jpg)
then not only will they appreciate that their outcomes depend on how others behave, but they
will take this into account in planning their own actions. As a result, models of networked
behavior must take strategic behavior and strategic reasoning into account.
A fundamental point here is that in a network setting, you should evaluate your actions
not in isolation, but with the expectation that the world will react to what you do. This
means that cause-effect relationships can become quite subtle. Changes in a product, a Web
site, or a government program can seem like good ideas when evaluated on the assumption
that everything else will remain static, but in reality such changes can easily create incentives
that shift behavior across the network in ways that were initially unintended.
Moreover, such effects are at work whether we are able to see the network or not. When
a large group of people is tightly interconnected, they will often respond in complex ways
that are only apparent at the population level, even though these effects may come from
implicit networks that we do not directly observe. Consider, for example, the way in which
new products, Web sites, or celebrities rise to prominence — as illustrated, for example, by
Figures 1.5 and 1.6, which show the growth in popularity of the social media sites YouTube
red vs blue political blogs - 2004 US campaign
capital, revenue and board members in the top 400 US companies
questions ...
what’s a node? an agent, a country, a molecule?
statistical correlation to non observablesfrom features of the network?
what to measure, local and global propertieshow connected, how resilient is a networkdo we have useful modular decompositions
how does a network happen, growth scenariohow does it evolve, rewiring scenario?
what kind of dynamics is there on the network - how stable?how well, fast, far do signal propagate and which signal?
what is an edge - transient/permanent - coarse-grained?
3.6. ADVANCED MATERIAL: BETWEENNESS MEASURES AND GRAPH PARTITIONING71
27
15
23
10 20
4
13
16
34
31
14
12
18
17
30
33
32
9
2
1
5
6
21
24
25
3
8
22
11
7
19
28
29
26
Figure 3.13: A karate club studied by Wayne Zachary [421] — a dispute during the courseof the study caused it to split into two clubs. Could the boundaries of the two clubs bepredicted from the network structure?
A second example, in Figure 3.13, is a picture of the social network of a karate club studied
by Wayne Zachary [421] and discussed in Chapter 1: a dispute between the club president
(node 34) and the instructor (node 1) led the club to split into two. Figure 3.13 shows the
network structure, with the membership in the two clubs after the division indicated by the
shaded and unshaded nodes. Now, a natural question is whether the structure itself contains
enough information to predict the fault line. In other words, did the split occur along a weak
interface between two densely connected regions? Unlike the network in Figure 3.12, or in
some of the earlier examples in the chapter, the two conflicting groups here are still heavily
interconnected. So to identify the division in this case, we need to look for more subtle
signals in the way in which edges between the groups effectively occur at lower “density”
than edges within the groups. We will see that this is in fact possible, both for the definitions
we consider here as well as other definitions.
A. A Method for Graph Partitioning
Many different approaches have been developed for the problem of graph partitioning, and
for networks with clear divisions into tightly-knit regions, there is often a wide range of
methods that will prove to be effective. While these methods can differ considerably in their
specifics, it is useful to identify the different general styles that motivate their designs.
the karate club divide one can see stress and fragility ... not very long after the secession happened almost along the expected faultline
diplomatic alliances
progressive shift to a balanced +- networks
5.3. APPLICATIONS OF STRUCTURAL BALANCE 127
GB
Fr
Ru
AH
Ge
It
(a) Three Emperors’ League 1872–81
GB
Fr
Ru
AH
Ge
It
(b) Triple Alliance 1882
GB
Fr
Ru
AH
Ge
It
(c) German-Russian Lapse 1890
GB
Fr
Ru
AH
Ge
It
(d) French-Russian Alliance 1891–94
GB
Fr
Ru
AH
Ge
It
(e) Entente Cordiale 1904
GB
Fr
Ru
AH
Ge
It
(f) British Russian Alliance 1907
Figure 5.5: The evolution of alliances in Europe, 1872-1907 (the nations GB, Fr, Ru, It, Ge,
and AH are Great Britain, France, Russia, Italy, Germany, and Austria-Hungary respec-
tively). Solid dark edges indicate friendship while dotted red edges indicate enmity. Note
how the network slides into a balanced labeling — and into World War I. This figure and
example are from Antal, Krapivsky, and Redner [20].
was China’s enemy, China was India’s foe, and India had traditionally bad relations with
Pakistan. Since the U.S. was at that time improving its relations with China, it supported
the enemies of China’s enemies. Further reverberations of this strange political constellation
became inevitable: North Vietnam made friendly gestures toward India, Pakistan severed
diplomatic relations with those countries of the Eastern Bloc which recognized Bangladesh,
and China vetoed the acceptance of Bangladesh into the U.N.”
Antal, Krapivsky, and Redner use the shifting alliances preceding World War I as another
example of structural balance in international relations — see Figure 5.5. This also reinforces
the fact that structural balance is not necessarily a good thing: since its global outcome is
often two implacably opposed alliances, the search for balance in a system can sometimes
be seen as a slide into a hard-to-resolve opposition between two sides.
5.3. APPLICATIONS OF STRUCTURAL BALANCE 127
GB
Fr
Ru
AH
Ge
It
(a) Three Emperors’ League 1872–81
GB
Fr
Ru
AH
Ge
It
(b) Triple Alliance 1882
GB
Fr
Ru
AH
Ge
It
(c) German-Russian Lapse 1890
GB
Fr
Ru
AH
Ge
It
(d) French-Russian Alliance 1891–94
GB
Fr
Ru
AH
Ge
It
(e) Entente Cordiale 1904
GB
Fr
Ru
AH
Ge
It
(f) British Russian Alliance 1907
Figure 5.5: The evolution of alliances in Europe, 1872-1907 (the nations GB, Fr, Ru, It, Ge,
and AH are Great Britain, France, Russia, Italy, Germany, and Austria-Hungary respec-
tively). Solid dark edges indicate friendship while dotted red edges indicate enmity. Note
how the network slides into a balanced labeling — and into World War I. This figure and
example are from Antal, Krapivsky, and Redner [20].
was China’s enemy, China was India’s foe, and India had traditionally bad relations with
Pakistan. Since the U.S. was at that time improving its relations with China, it supported
the enemies of China’s enemies. Further reverberations of this strange political constellation
became inevitable: North Vietnam made friendly gestures toward India, Pakistan severed
diplomatic relations with those countries of the Eastern Bloc which recognized Bangladesh,
and China vetoed the acceptance of Bangladesh into the U.N.”
Antal, Krapivsky, and Redner use the shifting alliances preceding World War I as another
example of structural balance in international relations — see Figure 5.5. This also reinforces
the fact that structural balance is not necessarily a good thing: since its global outcome is
often two implacably opposed alliances, the search for balance in a system can sometimes
be seen as a slide into a hard-to-resolve opposition between two sides.
structures ...
614 CHAPTER 20. THE SMALL-WORLD PHENOMENON
(a) Nodes arranged in a grid (b) A network built from local structure and random edges
Figure 20.2: The Watts-Strogatz model arises from a highly clustered network (such as the
grid), with a small number of random links added in.
and 20.1(b). And, indeed, at an implicit level, this is a large part of what makes the small-
world phenomenon surprising to many people when they first hear it: the social network
appears from the local perspective of any one individual to be highly clustered, not the kind
of massively branching structure that would more obviously reach many nodes along very
short paths.
The Watts-Strogatz model. Can we make up a simple model that exhibits both of the
features we’ve been discussing: many closed triads, but also very short paths? In 1998,
Duncan Watts and Steve Strogatz argued [411] that such a model follows naturally from a
combination of two basic social-network ideas that we saw in Chapters 3 and 4: homophily
(the principle that we connect to others who are like ourselves) and weak ties (the links to
acquaintances that connect us to parts of the network that would otherwise be far away).
Homophily creates many triangles, while the weak ties still produce the kind of widely
branching structure that reaches many nodes in a few steps.
Watts and Strogatz made this proposal concrete in a very simple model that generates
random networks with the desired properties. Paraphrasing their original formulation slightly
(but keeping the main idea intact), let’s suppose that everyone lives on a two-dimensional
grid — we can imagine the grid as a model of geographic proximity, or potentially some
more abstract kind of social proximity, but in any case a notion of similarity that guides the
formation of links. Figure 20.2(a) shows the set of nodes arranged on a grid; we say that
clustering and short distances
local ties and (small amount of) random ones
632 CHAPTER 20. THE SMALL-WORLD PHENOMENON
ab
c
d
e
f
g
hi
j
k
l
m
n
o
p
Figure 20.15: In myopic search, the current message-holder chooses the contact that lies
closest to the target (as measured on the ring), and it forwards the message to this contact.
A. The Optimal Exponent in One Dimension
Here, then, is the model we will be looking at. A set of n nodes are arranged on a one-
dimensional ring as shown in Figure 20.14(a), with each node connected by directed edges
to the two others immediately adjacent to it. Each node v also has a single directed edge
to some other node on the ring; the probability that v links to any particular node w is
proportional to d(v, w)−1
, where d(v, w) is their distance apart on the ring. We will call the
nodes to which v has an edge its contacts: the two nodes adjacent to it on the ring are its
local contacts, and the other one is its long-range contact. The overall structure is thus a ring
that is augmented with random edges, as shown in Figure 20.14(b). Again, this is essentially
just a one-dimensional version of the grid with random edges that we saw in Figure 20.5.1
Myopic Search. Let’s choose a random start node s and a random target node t on this
augmented ring network. The goal, as in the Milgram experiment, is to forward a message
from the start to the target, with each intermediate node on the way only knowing the
locations of its own neighbors, and the location of t, but nothing else about the full network.
The forwarding strategy that we analyze, which works well on the ring when q = 1, is a
1We could also analyze a model in which nodes have more outgoing edges, but this only makes the searchproblem easier; our result here will show that even when each node has only two local contacts and a singlelong-range contact, search can still be very efficient.
myopic decentralized search: from a to i
models ...
The spread of mobile viruses is aided by twodominant communication protocols. First, aBluetooth (BT) virus can infect all BT-activatedphones within a distance from 10 to 30 m, result-ing in a spatially localized spreading patternsimilar to the one observed in the case of influ-enza (3, 6, 7), severe acute respiratory syndrome(SARS) (8, 9), and other contact-based diseases(Fig. 1A) (10). Second, a multimedia messagingsystem (MMS) virus can send a copy of itself toall mobile phones whose numbers are found inthe infected phone’s address book, a long-rangespreading pattern previously exploited only bycomputer viruses (11, 12). Thus, in order to quan-titatively study the spreading dynamics of mobileviruses we need to simultaneously track the lo-cation (13), the mobility (14–17), and the com-munication patterns (18–21) ofmobile phone users.We achieved this by studying the anonymizedbilling record of a mobile phone provider andrecording the calling patterns and the coordinatesof the closest mobile phone tower each time agroup of 6.2 million mobile subscribers used
their phone. Thus, we do not know the users’precise locations within the tower’s receptionarea, and no information is available about theusers between calls.
The methods we used to simulate thespreading of a potential BT and MMS virus aredescribed in (22). Briefly, once a phone becomesinfected with an MMS virus, within 2 min itsends a copy of itself to each mobile phonenumber found in the handset’s phone book,approximated with the list of numbers withwhich the handset’s user communicated duringa month-long observational period. A BT viruscan infect only mobile phones within a distancer =10 m. To simulate this process, we assigned toeach user an hourly location that was consistentwith its travel patterns (13) and followed the in-fection dynamics within each mobile tower areausing the susceptible infected (SI) model (23).That is, we consider that an infected user (I ) in-fects a susceptible user (S), so that the number ofinfected users evolves in time (t) as dI/dt = bSI/N,where the effective infection rate isb = m<k>with
m = 1, N is the number of users in the tower area,and the average number of contacts is <k> = rA =NA/Atower, where A = pr2 represents the BT com-munication area and r = N/Atower is the popula-tion density inside a tower’s service area. Oncean infected user moves into the vicinity of a newtower, it will serve as a source of a BT infection inits new location.
A cell phone virus can infect only the phoneswith the operating system (OS) for which it wasdesigned (2, 3), making the market sharem of anOS an important free parameter in our study. Thecurrent market share of various smart phone OSsvary widely, from as little as 2.6% for PalmOS to64.3% for Symbian. Given that smart phonestogether represent less than 5% of all phones, theoverall market share of these OSs among all mo-bile phones is in the range ofm = 0.0013 for PalmOS andm = 0.032 for Symbian, numbers that areexpected to dramatically increase as smart phonesreplace traditional phones. To maintain the gen-erality of our results, we treatm as a free param-eter, finding that the spreading of both BT and
Fig. 1. The spread-ing mechanisms ofmobile viruses. (A) ABT virus can infect allphones found withinBT range from the in-fected phone, its spreadbeing determined bythe owner’s mobilitypatterns. An MMS viruscan infect all suscep-tible phones whosenumber is found inthe infected phone’sphonebook, resulting ina long-range spread-ing pattern that isindependent of theinfected phone’s phys-ical location. (B) Asmall neighborhoodof the call graph con-structed starting froma randomly chosen userand including all mo-bile phone contacts upto four degrees from it.The color of the noderepresents the hand-set’s OS, which in thisexample are randomlyassigned so that 75%of the nodes representOS1, and the red arethe remaining handsetswith OS2 (25%). (C)The clusters in the callgraph on which anMMS virus affecting agiven OS can spread,illustrating that anMMSvirus can reach at most the number of users that are part of the giant component of the appropriate handset. As the example for the OS shows, the size of thegiant component highly depends on the handset’s market share (see also Fig. 2C).
B OS1: 75% market share
OS2: 25% market share
Giant component80%
Giant component6%
Small connected components and single nodes
A Bluetooth (BT) contagion Multimedia messages (MMS) contagion
Bluetooth range (~ 10 m)
MMS messages
Bluetooth messages
C
BT susceptible phone
Phone out of Bluetooth range
MMS susceptible phoneInfected phone
22 MAY 2009 VOL 324 SCIENCE www.sciencemag.org1072
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propagation models under various assumptions
can we trust network-based models?
but ...
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pD Sexual Contact Network
a time-aggregated network of sexual contacts not a good model
everyone may become infected or no one may be infected, depending on:- edge duration- deviation on time of onset
Science (2009) vol. 325 (5939) pp. 414-416
information ...
patterns of socio-techno-eco-interactions with the increasingly computational and digital nature of modern world, there is more of these patterns
suppose you receive quick callbacks, call other people late at night, get more calls at social times
Finding them has become a profitable business
Social network analysis
even if eventually everyone knows (??), info can be scarce at micro time scales
fine time-structure of local information propagation
friction, a sort of illiquidity of info - so there should be an information market?
Too much information; nodes have limited resources to process information
reward for propagating accurately, relevantly (Gricean maxims of conversation apply?)what needs to be propagated? differentially as a function of the “power” of nodes, their neighbour’s tastes? exponential decrease of influence (`a la Maslov)?
randomness of encounters seems hard to control as well
can one enginer opinions and their propagation?
truthy.com