Table Of ContentLecture Notes in Economics
and Mathematical Systems 613
FoundingEditors:
M.Beckmann
H.P.Künzi
ManagingEditors:
Prof.Dr.G.Fandel
FachbereichWirtschaftswissenschaften
FernuniversitätHagen
Feithstr.140/AVZII,58084Hagen,Germany
Prof.Dr.W.Trockel
InstitutfürMathematischeWirtschaftsforschung(IMW)
UniversitätBielefeld
Universitätsstr.25,33615Bielefeld,Germany
EditorialBoard:
A.Basile,A.Drexl,H.Dawid,K.Inderfurth,W.Kürsten
. .
Ahmad K. Naimzada Silvana Stefani
Anna Torriero (Eds.)
Networks, Topology
and Dynamics
Theory and Applications
to Economics and Social Systems
ABC
Prof. Ahmad K. Naimzada Prof. Anna Torriero
Università degli Studi di Università Cattolica del Sarcro
Milano-Bicocca Cuore
Dipto. Economia Politica Largo A. Gemelli, 1
Piazza dell' Ateneo Nuovo, 1 20123 Milano
20126Milano Italy
Italy [email protected]
[email protected]
Prof. Silvana Stefani
Università degli Studi di
Milano-Bicocca
Dipto. Economia Politica
Piazza dell' Ateneo Nuovo, 1
20126 Milano
Italy
[email protected]
ISBN978-3-540-68407-7 e-ISBN978-3-540-68409-1
DOI10.1007/978-3-540-68409-1
LectureNotesinEconomicsandMathematicalSystemsISSN0075-8442
LibraryofCongressControlNumber:2008928718
The volume has been published with the financial contribution of the Quantitative Methods Depart-
ment of the University of Milano-Bicocca, Italy.
© 2009 Springer-Verlag Berlin Heidelberg
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, b roadcasting,
reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication
or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,
1965, in its current version, and permissions for use must always be obtained from Springer-Verlag.
Violations are liable for prosecution under the German Copyright Law.
The use of general descriptive names, registered names, trademarks, etc. in this publication does not
imply, even in the absence of a specific statement, that such names are exempt from the relevant
p rotective laws and regulations and therefore free for general use.
Cover design: WMXDesign GmbH, Heidelberg
Printed on acid-free paper
9 8 7 6 5 4 3 2 1
springer.com
Preface
There is convergent consensus among scientists that many social, economic and
financial phenomena can be described by a network of agents and their interac-
tions.Surprisingly,eventhoughtheapplicationfieldsarequitedifferent,thosenet-
worksoftenshowacommonbehaviour.Thus,theirtopologicalpropertiescangive
useful insights on how the network is structured, which are the most “important”
nodes/agents,howthenetworkreactstonewarrivals.Moreoverthenetwork,once
includedintoadynamiccontext,helpstomodelmanyphenomena.Amongthetop-
ics in which topology and dynamics are the essential tools, we will focus on the
diffusion of technologies and fads, the rise of industrial districts, the evolution of
financial markets, cooperation and competition, information flows, centrality and
prestige.
Thevolume,includingrecentcontributionstothefieldofnetworkmodelling,is
based on the communications presented at NET 2006 (Verbania, Italy) and NET
2007 (Urbino, Italy); offers a wide range of recent advances, both theoretical and
methodological,thatwillinterestacademicsaswellaspractitioners.
Theoryandapplicationsarenicelyintegrated:theoreticalpapersdealwithgraph
theory,gametheory,coalitions,dynamics,consumerbehavior,segregationmodels
andnewcontributionstotheabovementionedarea.Theapplicationscoverawide
range:airlinetransportation,financialmarkets,workteamorganization,labourand
creditmarket.
The volume can be used as a reference book for graduate and postgraduate
coursesonNetworkTheoryandComplexSystemsinFacultiesofEconomics,Math-
ematics, Engineering and Social Sciences. In Part I, the invited tutorials introduce
GraphTheoryfromthetheoreticalpointofview(Marusic)andthepossibleappli-
cationstoeconomics(Battiston).InPartII,thecontributionscoverlocalandglobal
interaction,complexbehavior,networkgames,whileinPartIIItheyrefertoMarkov
chainsandtopology.TheapplicationsareallplacedinPartIV.
Fifteenpapershavebeenselectedamongroughlythirtysubmittedextendedab-
stracts; each paper has been reviewed by two referees. Space limitations are the
mainreasonwhynomorepapershavebeenaccepted,althoughmanyofthemwere
reallyinteresting.
v
vi Preface
We are grateful to the scholars who have made NET 2006, NET 2007 and this
bookpossible,tothemembersofthescientificcommitteesofthetwoconferences
andthereferees:
• Gian-ItaloBISCHI–UniversityofUrbino,Italy
• SergioCURARINI–UniversityofVenice,Italy
• DomenicoDELLIGATTI–CatholicUniversityofMilan,Italy
• AndreaDEMONTIS–UniversityofSassari,Italy
• MauroGALLEGATI–UniversityofAncona,Italy
• LauraGARDINI–UniversityofUrbino,Italy
• RosannaGRASSI–UniversityofMilan-Bicocca,Italy
• JosefLAURI–UniversityofMalta,Malta
• RaimondoMANCA–UniversityofRome“LaSapienza”,Italy
• MarcoA.MARINI–UniversityofUrbino,Italy
• DraganMARUSIC–UniversityofPrimorskaandLiublijana,Slovenia
• FaustoMIGNANEGO–CatholicUniversity,Italy
• AntonioPALESTRINI–UniversityofTeramo,Italy
• ArturoPATARNELLO–UniversityofMilan-Bicocca,Italy
• AuraREGGIANI–UniversityofBologna,Italy
• MassimoRICOTTILLI–UniversityofBologna,Italy
• GiuliaRIVELLINI–CatholicUniversityofMilan,Italy
• PierluigiSACCO–IUAVVenezia,Italy
• RaffaeleSCAPELLATO–PolytechnicofMilan,Italy
• ChristosH.SKIADAS–TechnicalUniversityofCrete,Greece
• FabioTRAMONTANA–MarchePolytechnicUniversity,Italy
• GiovanniZAMBRUNO–UniversityofMilan-Bicocca,Italy
• LucaZARRI–UniversityofVerona,Italy
Finally, we would like to acknowledge the support, hospitality and encourage-
mentofthefollowinginstitutions:
– Dipartimento di Metodi Quantitativi per le Scienze Economiche e Aziendali,
Universita` degliStudidiMilano-Bicocca,
– DipartimentodiDisciplineMatematiche,FinanzaMatematicaedEconometria,
Universita` CattolicadiMilano
– IstitutodiScienzeEconomiche,Universita` degliStudidiUrbino.
March2008 AhmadK.Naimzada
Milan SilvanaStefani
AnnaTorriero
Contents
PartI Tutorials
SomeTopicsinGraphTheory..................................... 3
KlavdijaKutnarandDraganMarusˇicˇ
FromGraphTheorytoModelsofEconomicNetworks.ATutorial ...... 23
MichaelD.Ko¨nigandStefanoBattiston
PartII StrategicInteraction,EconomicModelsandNetworks
GamesofCoalitionandNetworkFormation:ASurvey................ 67
MarcoA.Marini
NetworkFormationwithClosenessIncentives ....................... 95
BernoBuechel
ADynamicModelofSegregationinSmall-WorldNetworks............ 111
GiorgioFagiolo,MarcoValente,andNicolaasJ.Vriend
InterdependentPreferences....................................... 127
AhmadK.NaimzadaandFabioTramontana
Co-EvolutiveModelsforFirmsDynamics ........................... 143
GiuliaRotundoandAndreaScozzari
PartIII MarkovChainsandTopology
BetweennessCentrality:ExtremalValuesandStructuralProperties..... 161
R.Grassi,R.Scapellato,S.Stefani,andA.Torriero
HowtoReduceUnnecessaryNoiseinTargetedNetworks .............. 177
GiacomoAlettiandDianeSaada
vii
viii Contents
The DynamicBehaviourofNon-HomogeneousSingle-Unireducible
MarkovandSemi-MarkovChains ................................. 195
GuglielmoD’Amico,JacquesJanssen,andRaimondoManca
PartIV Applications
ShareholdingNetworksandCentrality:AnApplicationtotheItalian
FinancialMarket................................................ 215
M.D’Errico,R.Grassi,andS.Stefani,andA.Torriero
NetworkDynamicswhenSelectingWorkTeamMembers.............. 229
AriannaDalFornoandUgoMerlone
Empirical Analysis of the Architecture of the Interbank Market
andCreditMarketUsingNetworkTheory .......................... 241
GiuliaDeMasi
NetworkMeasuresinCivilAirTransport:ACaseStudyofLufthansa... 257
AuraReggiani,SaraSignoretti,PeterNijkamp,andAlessandroCento
OnCertainGraphTheoryApplications............................. 283
KlavdijaKutnarandDraganMarusˇicˇ
Part I
Tutorials
Some Topics in Graph Theory
KlavdijaKutnarandDraganMarusˇicˇ
AbstractInthisshortintroductorycoursetographtheory,possiblyoneofthemost
propulsive areas of contemporarymathematics, some of the basic graph-theoretic
conceptstogetherwithsomeopenproblemsinthisscientificfieldarepresented.
1 SomeBasicConcepts
A simple graph X is an orderedpair of sets X =(V,E). Elements ofV are called
verticesofX andelementsofE arecallededgesofX.Anedgejoinstwovertices,
calleditsendvertices.Formally,wecanthinkoftheelementsofEassubsetsofV of
size2.Asimplegraphisthusanundirectedgraphwithnoloopsormultipleedges.
Ifu(cid:1)=vareverticesofasimplegraphX and{u,v}(sometimesshortenedtouv)
isanedgeofX,thenthisedgeissaidtobeincidenttouandv.Equivalently,uand
varesaidtobeadjacentorneighbors,andwewriteu∼v.Phraseslike,“anedge
joinsuandv”and“theedgebetweenuandv”arealsocommonlyused.
Graphscanbenicelyrepresentedwith diagramsconsistingofdotsstandingfor
verticesandlinesstandingforedges(seeFig.1).
Inasimplegraphthereisatmostoneedgejoiningapairofvertices.Inamulti-
graph, multiple edges are permitted between pairs of vertices. There may also be
edges,calledloops,thatconnectavertextoitself(seeFig.2).
As opposedto asimple graphwhereedgesare undirected,adirectedgraph(in
short,digraph)isanorderedpairofsets(V,E)whereV isasetofverticesandE is
K.Kutnar
UniversityofPrimorska,FAMNIT,Glagoljasˇka8,6000Koper,Slovenia
[email protected]
D.Marusˇicˇ
University of Primorska, FAMNIT, Glagoljasˇka 8, 6000 Koper, Slovenia and University of
Ljubljana,IMFM,Jadranska19,1000Ljubljana,Slovenia
[email protected]
A.K.Naimzadaetal.(eds.),Networks,TopologyandDynamics, 3
LectureNotesinEconomicsandMathematicalSystems613,
(cid:1)c Springer-VerlagBerlinHeidelberg2009
4 K.Kutnar,D.Marusˇicˇ
Fig. 1 A diagram of a
graph X =(V,E) where
V ={1,2,3,4} and E =
{{1,2},{1,3},{2,3},{3,4}}
Fig. 2 An example of a 1
multigraphwiththreeedges
betweenvertices1and2and 3
looponvertex3
4
2
Fig.3 Adirectedgraph 1
6 2
5 3
4
Fig.4 Aweightedgraph 1 10 2
6
5
3 3 4
a subsetof orderedpairsof verticesfromV. Now the edgesmaybe thoughtofas
arrowsgoingfromatail(vertex)toahead(vertex)(seeFig.3).
Sometimesitis usefulto associate a number,oftencalledits weight, with each
edgeinagraph.Suchgraphsarecallededge-weightedorsimplyweightedgraphs;
theymaybesimple,directed,etc.(seeFig.4).
From now on by a graph we shall mean a simple and, unless otherwise speci-
fied,finite,undirectedandconnectedgraph.LetX =(V,E)beagraph.Thedegree
d(v)ofavertexv∈V isthenumberofedgeswithwhichitisincident.Thesetof
