Overview of Overview of Outline Complex Networks Complex Networks Complex Networks Principles of Complex Systems Basic definitions Basic definitions Basic definitions Examples of Examples of Course CSYS/MATH 300, Fall, 2009 Complex Networks Complex Networks Examples of Complex Networks Properties of Properties of Complex Networks Complex Networks Prof. Peter Dodds Nutshell Nutshell Properties of Complex Networks Basic models of Basic models of complex networks complex networks Dept. of Mathematics & Statistics Generalized random Generalized random Nutshell networks networks Center for Complex Systems :: Vermont Advanced Computing Center Scale-free networks Scale-free networks University of Vermont Small-world networks Small-world networks Generalized affiliation Generalized affiliation Basic models of complex networks networks networks References Generalized random networks References Scale-free networks Small-world networks Generalized affiliation networks References Frame 1/122 Frame 2/122 Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License . net • work |ˈnetˌwərk| Overview of Overview of Thesaurus deliciousness: Complex Networks Complex Networks noun 1 an arrangement of intersecting horizontal and vertical lines. Basic definitions Basic definitions • a complex system of roads, railroads, or other transportation routes : a network of railroads. Examples of Examples of Complex Networks Complex Networks 2 a group or system of interconnected people or things : a trade network. • a group of people who exchange information, contacts, and Properties of Properties of network Complex Networks Complex Networks experience for professional or social purposes : a support network. Nutshell Nutshell • a group of broadcasting stations that connect for the simultaneous noun broadcast of a program : the introduction of a second TV network | [as adj. ] Basic models of Basic models of 1 a network of arteries WEB , lattice, net, matrix, mesh, complex networks complex networks network television. Generalized random Generalized random • a number of interconnected computers, machines, or operations : crisscross, grid, reticulum, reticulation; Anatomy plexus. networks networks Scale-free networks Scale-free networks specialized computers that manage multiple outside connections to a network | a 2 a network of lanes MAZE , labyrinth, warren, tangle. Small-world networks Small-world networks local cellular phone network. Generalized affiliation Generalized affiliation networks networks 3 a network of friends SYSTEM , complex, nexus, web, • a system of connected electrical conductors. References References webwork. verb [ trans. ] connect as or operate with a network : the stock exchanges have proven to be resourceful in networking these deals. • link (machines, esp. computers) to operate interactively : [as adj. ] ( networked ) networked workstations. • [ intrans. ] [often as n. ] ( networking ) interact with other people to exchange information and develop contacts, esp. to further one's career : the skills of networking, bargaining, and negotiation. Frame 3/122 Frame 4/122
Overview of Overview of Ancestry: Ancestry: Complex Networks Complex Networks Basic definitions Basic definitions Examples of Examples of Complex Networks First known use: Geneva Bible, 1560 Complex Networks From Keith Briggs’s excellent Properties of Properties of etymological investigation: ( ⊞ ) ‘And thou shalt make unto it a grate like networke of Complex Networks Complex Networks brass (Exodus xxvii 4).’ Nutshell Nutshell Basic models of Basic models of complex networks From the OED via Briggs: complex networks Generalized random Generalized random networks networks Scale-free networks Scale-free networks ◮ 1658–: reticulate structures in animals Small-world networks Small-world networks ◮ Opus reticulatum: Generalized affiliation Generalized affiliation networks ◮ 1839–: rivers and canals networks ◮ A Latin origin? References References ◮ 1869–: railways ◮ 1883–: distribution network of electrical cables ◮ 1914–: wireless broadcasting networks [http://serialconsign.com/2007/11/we-put-net-network] Frame 5/122 Frame 6/122 Overview of Overview of Ancestry: Key Observation: Complex Networks Complex Networks ◮ Many complex systems Basic definitions Basic definitions Net and Work are venerable old words: can be viewed as complex networks Examples of Examples of Complex Networks Complex Networks ◮ ‘Net’ first used to mean spider web (King Ælfréd, 888) . of physical or abstract interactions. Properties of Properties of ◮ ‘Work’ appear to have long meant purposeful action. Complex Networks Complex Networks ◮ Opens door to mathematical and numerical analysis. Nutshell Nutshell ◮ Dominant approach of last decade of a Basic models of Basic models of complex networks theoretical-physics/stat-mechish flavor. complex networks Generalized random Generalized random networks networks ◮ Mindboggling amount of work published on complex Scale-free networks Scale-free networks Small-world networks Small-world networks networks since 1998... Generalized affiliation Generalized affiliation networks networks ◮ ... largely due to your typical theoretical physicist: References References ◮ Piranha physicus ◮ ‘Network’ = something built based on the idea of ◮ Hunt in packs. natural, flexible lattice or web. ◮ Feast on new and interesting ideas ◮ c.f., ironwork, stonework, fretwork. (see chaos, cellular automata, ...) Frame 7/122 Frame 8/122
Overview of Overview of Popularity (according to ISI) Popularity according to books: Complex Networks Complex Networks Basic definitions Basic definitions “Collective dynamics of ‘small-world’ networks” [28] Examples of Examples of Complex Networks Complex Networks ◮ Watts and Strogatz Properties of Properties of Complex Networks The Tipping Point: How Little Things can Complex Networks Nature, 1998 make a Big Difference—Malcolm Gladwell [12] Nutshell Nutshell ◮ ≈ 3752 citations (as of June 5, 2009) Basic models of Basic models of complex networks complex networks ◮ Over 1100 citations in 2008 alone. Generalized random Generalized random networks networks Scale-free networks Scale-free networks Small-world networks Small-world networks Generalized affiliation Generalized affiliation “Emergence of scaling in random networks” [3] networks networks References References Nexus: Small Worlds and the Groundbreaking ◮ Barabási and Albert Science of Networks—Mark Buchanan Science, 1999 ◮ ≈ 3860 citations (as of June 5, 2009) ◮ Over 1100 citations in 2008 alone. Frame 9/122 Frame 10/122 Overview of Overview of Popularity according to books: Numerous others: Complex Networks Complex Networks ◮ Complex Social Networks—F. Vega-Redondo [25] Basic definitions Basic definitions ◮ Fractal River Basins: Chance and Self-Organization—I. Examples of Examples of Complex Networks Complex Networks Rodríguez-Iturbe and A. Rinaldo [20] Properties of Properties of Linked: How Everything Is Connected to Complex Networks Complex Networks ◮ Random Graph Dynamics—R. Durette Everything Else and What It Nutshell Nutshell ◮ Scale-Free Networks—Guido Caldarelli Means—Albert-Laszlo Barabási Basic models of Basic models of complex networks complex networks ◮ Evolution and Structure of the Internet: A Statistical Generalized random Generalized random networks networks Physics Approach—Romu Pastor-Satorras and Scale-free networks Scale-free networks Small-world networks Small-world networks Alessandro Vespignani Generalized affiliation Generalized affiliation networks networks ◮ Complex Graphs and Networks—Fan Chung References References Six Degrees: The Science of a Connected ◮ Social Network Analysis—Stanley Wasserman and Age—Duncan Watts [26] Kathleen Faust ◮ Handbook of Graphs and Networks—Eds: Stefan Bornholdt and H. G. Schuster [6] ◮ Evolution of Networks—S. N. Dorogovtsev and J. F. F. Frame 11/122 Frame 12/122 Mendes [11]
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