Introduction to Network Science and Complex Systems

March 23, 2018

Rosen College of Hospitality Management

University of Central Florida

Jalayer (Jolly) Khalilzadeh, Ph.D. Candidate

CONTENT Bibliography: Network Footprint

Origins and History

Definitions and Terminology

Complexity & Complex Systems

Network Models

Conceptual Structure

Future: Potential Areas

Resources

BIBLIOGRAPHY: NETWORK FOOTPRINTArticles 175

Sources (Journals, Books, etc.) 51

Period 1985 - 2018

Average citations per article 21.93

Authors 326

Authors per Article 1.86

Year Articles2018 72017 342016 152015 172014 92013 142012 92011 172010 122009 62008 102007 42006 62005 42004 22003 12002 12001 12000 21999 11998 11997 11985 1

Growth: 9.25

BIBLIOGRAPHY: NETWORK FOOTPRINT

Source Articles

Tourism Management 21

Annals of Tourism Research 17

Current Issues in Tourism 10

Tourism Review 9

Asia Pacific Journal of Tourism Research 7

International Journal of Contemporary Hospitality Management 7

International Journal of Hospitality Management 7

Tourism Analysis 6

Tourism Geographies 6

International Journal of Tourism Research 5

(Mathematical Association of America (MAA), Euler Archive, 2018)

ORIGIN: SEVEN BRIDGES OF KÖNIGSBERG

Leonhard Euler1707-1783

ORIGIN: SEVEN BRIDGES OF KÖNIGSBERG

ORIGIN: SEVEN BRIDGES OF KÖNIGSBERG

a b c d e f

a 0 1 0 0 0 0

b 0 1 0 0 0 0

c 1 0 0 0 0 0

d 1 1 1 0 0 0

e 0 0 85 1 0 0

f 0 0 0 1 1 0

DEFINITIONS &TERMINOLOGY

Vertex, Node, Actor,Ego/Alter

Edge, Link, Arc

a

b

c

d

e

f

A B C D

A 0 1 1 1

B 1 0 0 1

C 1 0 0 1

D 1 1 1 0

85

= 1

= 2

= 3=

3

= 2 or 86 ?

a b c d e f g h i j

A 1 0 1 1 0 0 0 0 0 0

B 1 1 0 0 0 1 1 0 0 1

C 1 1 0 0 0 0 0 0 1 0

D 0 0 0 0 1 0 0 1 0 0

DEFINITIONS &TERMINOLOGY

a

A

B

C

bc

df

g

i

j

D

e

h

𝐌×𝐌𝐓

Porter, M. A. (2018)

COMPLEXITY & COMPLEX SYSTEMSDefinition

o System

o Components (large number)

o Interaction

o Difficulty of behavior modeling

o Nonlinearity

o Spontaneous order

o Adaptation

o Feedback loops

Exampleso Brain

o Body

o Ecosystem

o City

o Economy

o Climate

Complex

Simple

Complicated

Chaos

NETWORK MODELS

Random Scale-Free Small-World ERGMs Dynamic

NETWORK MODELS

Random Scale-Free Small-World ERGMs Dynamic

Measures:

•Order (N): 400

•Size (E): 747

•Transitivity: 0.0074

•Average Distance: 4.6

•Density: 0.0094

•Mean Degree: 3.735

•Components: 11

NETWORK MODELS

Random Scale-Free Small-World ERGMs Dynamic

Measures:

•Order (N): 400

•Size (E): 399

•Transitivity: 0

•Average Distance: 7.32

•Density: 0.005

•Mean Degree: 1.995

•Components: 1

NETWORK MODELS

Random Scale-Free Small-World ERGMs Dynamic

Measures:

•Order (N): 400

•Size (E): 2800

•Transitivity: 0.55

•Average Distance: 3.34

•Density: 0.035

•Mean Degree: 14

•Components: 1

o Random Rewiring

COMPARATIVE ATTRIBUTESDistribution

Barabási, A. L., & Frangos, J. (2014)

Generative Networks

Generative Models PA Functions Fitness ReferenceGT model Free Free Pham et al.

Callaway et al. Ak = 1 ηi = 1 Callaway et al.

BA model Ak = k ηi = 1 Barabási and Albert

Extended BA model Ak = kα ηi = 1 Krapivsky et al.

Krapivsky et al. Free ηi = 1 Krapivsky et al.

Caldarelli model Ak = 1 Free Caldarelli et al.

BB model Ak = k Free Bianconi and Barabási

Extended BB model Ak = kα Free Not previously considered.

o Preferential attachment (PA) aka rich-get-richer

o Fitness aka fit-get-richer

COMPARATIVE ATTRIBUTES

Pham, T., Sheridan, P., & Shimodaira, H. (2016)

Simulation

Attack & Random Errors

COMPARATIVE ATTRIBUTES

o Percolation

• Site percolation• Bond percolation

Albert, R., Jeong, H., & Barabási, A. L. (2000)

3D Representation

⇝

COMPARATIVE ATTRIBUTESControlling the Network

𝑃 𝑥 = C𝑥−𝛾 , for x ≥ 𝑥𝑚𝑖𝑛

Liu, Y. Y., Slotine, J. J., & Barabási, A. L. (2011)

Type Name Order (N) Size (E) nDRegulatory TRN-Yeast-1 4,441 12,873 96.5%

Regulatory Ownership-USCorp 7,253 6,726 82.0%

World Wide Web nd.edu 325,729 1,497,134 67.7%

Trust WikiVote 7,115 103,689 66.6%

Internet p2p Gnutella 10,876 39,994 55.2%

Social communication Email-epoch 3,188 39,256 42.6%

Power grid Texas 4,889 5,855 32.5%

Food web Seagrass 49 226 26.5%

Electronic circuits s838 512 819 23.2%

Citation ArXiv-HepTh 27,770 352,807 21.6%

Social communication Cellphone 36,595 91,826 20.4%

Trust College student 32 96 18.8%

Neuronal Network Caenorhabditis elegans 297 2,345 16.5%

Trust Prison inmate 67 182 13.4%

Intra-organizational Consulting 46 879 4.3%

Intra-organizational Manufacturing 77 2,228 1.3%nD: Nodes (driver nodes) involved in the control process

⇝

COMPARATIVE ATTRIBUTESControlling the Network

𝑃 𝑥 = C𝑥−𝛾 , for x ≥ 𝑥𝑚𝑖𝑛

Liu, Y. Y., Slotine, J. J., & Barabási, A. L. (2011)

NETWORK MODELS

Random Scale-Free Small-World ERGMs Dynamic

Global Model

Local Model

NETWORK MODELS

Random Scale-Free Small-World ERGMs Dynamic

Susceptible-Infected(SI)

Susceptible-Infected-Recovered/Removed (SIR)

Susceptible-Infected-Recovered-Susceptible (SIRS)

Simulation

Newman, M. (2010)

CONCEPTUAL STRUCTUREKey Words Articles

NETWORK ANALYSIS 70

TOURISM 33

SOCIAL NETWORKS 27

SOCIAL NETWORK ANALYSIS 24

TOURISM MANAGEMENT 24

ACTOR NETWORK THEORY 18

NETWORK 15

TOURISM DEVELOPMENT 15

TOURIST DESTINATION 14

STAKEHOLDER 13

DESTINATION MANAGEMENT 11

TOURISM MARKET 10

SOCIAL CAPITAL 9

CHINA 7

INNOVATION 6

Castellani, B. (2018)

FUTURE: POTENTIAL AREAS

RESOURCESReference Books

o Newman, M. (2010). Networks: an introduction. Oxford university press.o Barabási, A. L. (2016). Network science. Cambridge university press.o Jackson, M. O. (2010). Social and economic networks. Princeton university press.o Scott, J., & Carrington, P. J. (2011). The SAGE handbook of social network analysis. SAGE publications.o Barabási, A. L., & Frangos, J. (2014). Linked: the new science of networks science of networks. Basic Books.o Watts, D. J. (2004). Six degrees: The science of a connected age. WW Norton & Company.o Christakis, N. A., & Fowler, J. H. (2009). Connected: The surprising power of our social networks and how they shape our

lives. Little, Brown.o Rainie, L., & Wellman, B. (2012). Networked: The new social operating system. Mit Press.o Barabási, A. L., & Gelman, A. (2010). Bursts: The hidden pattern behind everything we do. Physics Today, 63(5), 46.o Alhajj, R., & Rokne, J. (2014). Encyclopedia of social network analysis and mining. Springer Publishing Company,

Incorporated.o Barnett, G. A. (2011). Encyclopedia of social networks (Vol. 1). Sage.o Wasserman, S., & Faust, K. (1994). Social network analysis: Methods and applications (Vol. 8). Cambridge university

press.o Scott, N., Baggio, R., & Cooper, C. (2008). Network analysis and tourism: From theory to practice. Channel View

Publications.

RESOURCES

Instruction Books

o Luke, D. A. (2015). A user's guide to network analysis in R. London, England: Springer.o Harris, J. K. (2013). An introduction to exponential random graph modeling (Vol. 173). Sage Publications.o Nagarajan, R., Scutari, M., & Lèbre, S. (2013). Bayesian networks in R. Springer, 122, 125-127.o Kolaczyk, E. D., & Csárdi, G. (2014). Statistical analysis of network data with R (Vol. 65). New York: Springer.o De Nooy, W., Mrvar, A., & Batagelj, V. (2011). Exploratory social network analysis with Pajek (Vol. 27).

Cambridge University Press.

RESOURCESSoftware Packages

o Pajek (http://mrvar.fdv.uni-lj.si/pajek/) o Gephi (https://gephi.org/)o Statnet

• ergm• tergm• network• sna• tsna• degreenet• latentnet• networksis• networkDynamic• relevent• EpiModel

o igrapho netdiffuseRo Bergmo Rsienao btergmo Hergmo GERGMo PAFito ndtv

o https://github.com/briatte/awesome-network-analysis

http://mrvar.fdv.uni-lj.si/pajek/https://gephi.org/https://github.com/briatte/awesome-network-analysis

Thank You