network Complex Networks Complex Networks Prof. Peter Dodds - PDF document

Overview of Thesaurus deliciousness: Overview of Complex Networks Complex Networks Complex Networks Principles of Complex Systems Basic definitions Basic definitions Examples of Examples of CSYS/MATH 300, Fall, 2011 Complex Networks Complex Networks Properties of Properties of network Complex Networks Complex Networks Prof. Peter Dodds Nutshell Nutshell noun Basic models of Basic models of 1 a network of arteries WEB , lattice, net, matrix, mesh, complex networks complex networks Department of Mathematics & Statistics | Center for Complex Systems | Generalized random Generalized random crisscross, grid, reticulum, reticulation; Anatomy plexus. networks networks Vermont Advanced Computing Center | University of Vermont Scale-free networks Scale-free networks 2 a network of lanes MAZE , labyrinth, warren, tangle. Small-world networks Small-world networks Generalized affiliation Generalized affiliation networks networks 3 a network of friends SYSTEM , complex, nexus, web, References References webwork. Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License . 1 of 127 4 of 127 Outline Overview of Ancestry: Overview of Complex Networks Complex Networks Basic definitions Basic definitions Basic definitions Examples of Examples of Complex Networks Complex Networks From Keith Briggs’s excellent etymological Examples of Complex Networks Properties of Properties of investigation: ( ⊞ ) Complex Networks Complex Networks Nutshell Nutshell Properties of Complex Networks Basic models of Basic models of complex networks complex networks Generalized random Generalized random Nutshell networks networks Scale-free networks Scale-free networks Small-world networks Small-world networks ◮ Opus reticulatum: Generalized affiliation Generalized affiliation Basic models of complex networks networks networks ◮ A Latin origin? References References Generalized random networks Scale-free networks Small-world networks Generalized affiliation networks [http://serialconsign.com/2007/11/we-put-net-network] References 2 of 127 5 of 127 net • work |ˈnetˌwərk| Overview of Ancestry: Overview of 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 First known use: Geneva Bible, 1560 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 ‘And thou shalt make unto it a grate like networke of 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 brass (Exodus xxvii 4).’ broadcast of a program : the introduction of a second TV network | [as adj. ] Basic models of Basic models of complex networks complex networks network television. From the OED via Briggs: Generalized random Generalized random • a number of interconnected computers, machines, or operations : networks networks Scale-free networks Scale-free networks specialized computers that manage multiple outside connections to a network | a ◮ 1658–: reticulate structures in animals Small-world networks Small-world networks local cellular phone network. Generalized affiliation Generalized affiliation networks networks • a system of connected electrical conductors. ◮ 1839–: rivers and canals References References ◮ 1869–: railways verb [ trans. ] connect as or operate with a network : the stock exchanges have proven to be ◮ 1883–: distribution network of electrical cables resourceful in networking these deals. • link (machines, esp. computers) to operate interactively : [as adj. ] ( ◮ 1914–: wireless broadcasting networks 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. 3 of 127 6 of 127

Ancestry: Overview of Popularity (according to ISI) Overview of Complex Networks Complex Networks Basic definitions Basic definitions Net and Work are venerable old words: Examples of Examples of ◮ ‘Net’ first used to mean spider web (King Ælfréd, 888) . Complex Networks Complex Networks Review articles: Properties of Properties of ◮ ‘Work’ appear to have long meant purposeful action. Complex Networks Complex Networks ◮ S. Boccaletti et al. Nutshell Nutshell “Complex networks: structure and dynamics” [6] Basic models of Basic models of Times cited: 1,028 (as of June 7, 2010) complex networks complex networks Generalized random Generalized random networks ◮ M. Newman networks Scale-free networks Scale-free networks “The structure and function of complex networks” [21] Small-world networks Small-world networks Generalized affiliation Generalized affiliation networks networks Times cited: 2,559 (as of June 7, 2010) References References ◮ R. Albert and A.-L. Barabási “Statistical mechanics of complex networks” [2] ◮ ‘Network’ = something built based on the idea of Times cited: 3,995 (as of June 7, 2010) natural, flexible lattice or web. ◮ c.f., ironwork, stonework, fretwork. 7 of 127 10 of 127 Key Observation: Overview of Popularity according to textbooks: Overview of Complex Networks Complex Networks ◮ Many complex systems Basic definitions Basic definitions can be viewed as complex networks Examples of Examples of Complex Networks Complex Networks of physical or abstract interactions. Properties of Properties of ◮ Opens door to mathematical and numerical analysis. Complex Networks Complex Networks Textbooks: Nutshell Nutshell ◮ Dominant approach of last decade of a ◮ Mark Newman (Physics, Michigan) Basic models of Basic models of theoretical-physics/stat-mechish flavor. complex networks complex networks “Networks: An Introduction” ( ⊞ ) Generalized random Generalized random networks networks ◮ Mindboggling amount of work published on complex ◮ David Easley and Jon Kleinberg (Economics and Scale-free networks Scale-free networks Small-world networks Small-world networks networks since 1998... Computer Science, Cornell) Generalized affiliation Generalized affiliation networks networks “Networks, Crowds, and Markets: Reasoning About a ◮ ... largely due to your typical theoretical physicist: References References Highly Connected World” ( ⊞ ) ◮ Piranha physicus ◮ Hunt in packs. ◮ Feast on new and interesting ideas (see chaos, cellular automata, ...) 8 of 127 11 of 127 Popularity (according to ISI) Overview of Popularity according to books: Overview of Complex Networks Complex Networks Basic definitions Basic definitions Examples of Examples of “Collective dynamics of ‘small-world’ networks” [31] Complex Networks Complex Networks Properties of Properties of ◮ Watts and Strogatz The Tipping Point: How Little Things can Complex Networks Complex Networks Nature, 1998 make a Big Difference—Malcolm Gladwell [14] Nutshell Nutshell ◮ Cited ≈ 4325 times (as of June 7, 2010) Basic models of Basic models of complex networks complex networks Generalized random Generalized random ◮ Over 1100 citations in 2008 alone. networks networks Scale-free networks Scale-free networks Small-world networks Small-world networks Generalized affiliation Generalized affiliation “Emergence of scaling in random networks” [4] networks networks References References ◮ Barabási and Albert Nexus: Small Worlds and the Groundbreaking Science, 1999 Science of Networks—Mark Buchanan ◮ Cited ≈ 4769 times (as of June 7, 2010) ◮ Over 1100 citations in 2008 alone. 9 of 127 12 of 127