Overview Outline Overview Overview of Complex Networks Class admin Class admin Complex Networks, CSYS/MATH 303, Spring, 2010 Class admin Basic definitions Basic definitions Popularity Popularity Basic definitions Examples of Examples of Prof. Peter Dodds Complex Networks Complex Networks Properties of Properties of Popularity Complex Networks Complex Networks Department of Mathematics & Statistics Center for Complex Systems Modelling Complex Modelling Complex Networks Examples of Complex Networks Networks Vermont Advanced Computing Center University of Vermont Nutshell Nutshell References References Properties of Complex Networks Modelling Complex Networks Nutshell References Frame 1/61 Frame 2/61 Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License . Class Admin Overview Exciting details regarding these slides: Overview Class admin Class admin Basic definitions Basic definitions ◮ Three versions (all in pdf): Popularity Popularity 1. Presentation, Examples of Examples of Complex Networks Complex Networks 2. Flat Presentation, ◮ Office hours: Properties of Properties of 3. Handout (2x2). Complex Networks Complex Networks ◮ Tuesday 1:00 pm–2:30 pm (Farrell Hall) ◮ Presentation versions are navigable and hyperlinks Modelling Complex Modelling Complex ◮ Appointments by email. Networks Networks are clickable. ◮ Course outline Nutshell Nutshell ◮ Web links look like this ( ⊞ ). References References ◮ Projects ◮ References in slides link to full citation at end. [1] ◮ Citations contain links to papers in pdf (if available). ◮ Brought to you by a concoction of L A T EX, Beamer, and perl. Frame 3/61 Frame 4/61
Basic definitions Overview Basic definitions Overview Complex System—Some ingredients: Class admin Class admin Basic definitions Basic definitions ◮ Distributed system of many interrelated parts Popularity Popularity ◮ No centralized control Examples of Examples of Complex Networks Complex Networks ◮ Nonlinear relationships Complex: (Latin = with + fold/weave (com + plex)) Properties of Properties of Complex Networks Complex Networks ◮ Existence of feedback loops Adjective Modelling Complex Modelling Complex ◮ Made up of multiple parts; intricate or detailed. ◮ Complex systems are open (out of equilibrium) Networks Networks Nutshell Nutshell ◮ Not simple or straightforward. ◮ Presence of Memory References References ◮ Modular (nested)/multiscale structure ◮ Opaque boundaries ◮ Emergence—‘More is Different’ [1] ◮ Many phenomena can be complex: social, technical, informational, geophysical, meteorological, fluidic, ... Frame 5/61 Frame 6/61 net • work |ˈnetˌwərk| Overview Thesaurus deliciousness: Overview noun 1 an arrangement of intersecting horizontal and vertical lines. Class admin Class admin • a complex system of roads, railroads, or other transportation routes : a network of railroads. Basic definitions Basic definitions 2 a group or system of interconnected people or things : a trade network. Popularity Popularity • a group of people who exchange information, contacts, and Examples of network Examples of experience for professional or social purposes : a support network. Complex Networks Complex Networks • a group of broadcasting stations that connect for the simultaneous Properties of noun Properties of broadcast of a program : the introduction of a second TV network | [as adj. ] Complex Networks Complex Networks 1 a network of arteries WEB , lattice, net, matrix, mesh, network television. Modelling Complex Modelling Complex • a number of interconnected computers, machines, or operations : Networks Networks crisscross, grid, reticulum, reticulation; Anatomy plexus. specialized computers that manage multiple outside connections to a network | a Nutshell Nutshell 2 a network of lanes MAZE , labyrinth, warren, tangle. local cellular phone network. References References 3 a network of friends SYSTEM , complex, nexus, web, • a system of connected electrical conductors. 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 7/61 Frame 8/61
Ancestry: Overview Ancestry: Overview Class admin Class admin Basic definitions Basic definitions From Keith Briggs’s excellent First known use: Geneva Bible, 1560 Popularity Popularity etymological investigation: ( ⊞ ) Examples of ‘And thou shalt make unto it a grate like networke of Examples of Complex Networks Complex Networks brass (Exodus xxvii 4).’ Properties of Properties of Complex Networks Complex Networks From the OED via Briggs: Modelling Complex Modelling Complex Networks Networks ◮ 1658–: reticulate structures in animals Nutshell Nutshell ◮ Opus reticulatum: References References ◮ 1839–: rivers and canals ◮ A Latin origin? ◮ 1869–: railways ◮ 1883–: distribution network of electrical cables ◮ 1914–: wireless broadcasting networks [http://serialconsign.com/2007/11/we-put-net-network] Frame 9/61 Frame 10/61 Ancestry: Overview Key Observation: Overview ◮ Many complex systems Class admin Class admin Net and Work are venerable old words: can be viewed as complex networks Basic definitions Basic definitions ◮ ‘Net’ first used to mean spider web (King Ælfréd, 888) . Popularity Popularity of physical or abstract interactions. Examples of Examples of ◮ ‘Work’ appears to have long meant purposeful action. ◮ Opens door to mathematical and numerical analysis. Complex Networks Complex Networks Properties of Properties of ◮ Dominant approach of last decade of a Complex Networks Complex Networks theoretical-physics/stat-mechish flavor. Modelling Complex Modelling Complex Networks Networks ◮ Mindboggling amount of work published on complex Nutshell Nutshell networks since 1998... References References ◮ ... largely due to your typical theoretical physicist: ◮ 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 11/61 Frame 12/61
Popularity (according to ISI) Overview Popularity according to books: Overview Class admin Class admin “Collective dynamics of ‘small-world’ networks” [21] Basic definitions Basic definitions Popularity Popularity ◮ Watts and Strogatz Examples of Examples of The Tipping Point: How Little Things can Complex Networks Complex Networks Nature, 1998 make a Big Difference—Malcolm Gladwell [9] Properties of Properties of ◮ ≈ 4100 citations (as of January 18, 2010) Complex Networks Complex Networks Modelling Complex Modelling Complex ◮ Over 1100 citations in 2008 alone. Networks Networks Nutshell Nutshell “Emergence of scaling in random networks” [2] References References Nexus: Small Worlds and the Groundbreaking ◮ Barabási and Albert Science of Networks—Mark Buchanan Science, 1999 ◮ ≈ 4400 citations (as of January 18, 2010) ◮ Over 1100 citations in 2008 alone. Frame 13/61 Frame 14/61 Popularity according to books: Overview Numerous others: Overview ◮ Complex Social Networks—F. Vega-Redondo [18] Class admin Class admin ◮ Fractal River Basins: Chance and Self-Organization—I. Basic definitions Basic definitions Rodríguez-Iturbe and A. Rinaldo [15] Popularity Popularity Linked: How Everything Is Connected to Examples of Examples of ◮ Random Graph Dynamics—R. Durette Complex Networks Complex Networks Everything Else and What It Properties of Properties of ◮ Scale-Free Networks—Guido Caldarelli Means—Albert-Laszlo Barabási Complex Networks Complex Networks Modelling Complex Modelling Complex ◮ Evolution and Structure of the Internet: A Statistical Networks Networks Physics Approach—Romu Pastor-Satorras and Nutshell Nutshell Alessandro Vespignani References References ◮ Complex Graphs and Networks—Fan Chung Six Degrees: The Science of a Connected ◮ Social Network Analysis—Stanley Wasserman and Age—Duncan Watts [19] Kathleen Faust ◮ Handbook of Graphs and Networks—Eds: Stefan Bornholdt and H. G. Schuster [5] ◮ Evolution of Networks—S. N. Dorogovtsev and J. F. F. Frame 15/61 Frame 16/61 Mendes [8]
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