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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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