Overview Overview of Complex Networks Class admin Complex Networks, CSYS/MATH 303, Spring, 2010 Basic definitions Popularity Examples of Prof. Peter Dodds Complex Networks Properties of Complex Networks Department of Mathematics & Statistics Center for Complex Systems Modelling Complex Networks Vermont Advanced Computing Center University of Vermont Nutshell References Frame 1/61 Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License .
Overview Outline Class admin Class admin Basic definitions Popularity Basic definitions Examples of Complex Networks Properties of Popularity Complex Networks Modelling Complex Networks Examples of Complex Networks Nutshell References Properties of Complex Networks Modelling Complex Networks Nutshell References Frame 2/61
Overview Class Admin Class admin Basic definitions Popularity Examples of Complex Networks ◮ Office hours: Properties of Complex Networks ◮ Tuesday 1:00 pm–2:30 pm (Farrell Hall) Modelling Complex ◮ Appointments by email. Networks ◮ Course outline Nutshell References ◮ Projects Frame 3/61
Overview Exciting details regarding these slides: Class admin Basic definitions ◮ Three versions (all in pdf): Popularity 1. Presentation, Examples of Complex Networks 2. Flat Presentation, Properties of 3. Handout (2x2). Complex Networks ◮ Presentation versions are navigable and hyperlinks Modelling Complex Networks are clickable. Nutshell ◮ Web links look like this ( ⊞ ). References ◮ 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 4/61
Overview Basic definitions Complex System—Some ingredients: Class admin Basic definitions ◮ Distributed system of many interrelated parts Popularity ◮ No centralized control Examples of Complex Networks ◮ Nonlinear relationships Properties of Complex Networks ◮ Existence of feedback loops Modelling Complex ◮ Complex systems are open (out of equilibrium) Networks Nutshell ◮ Presence of Memory 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
Overview Basic definitions Class admin Basic definitions Popularity Examples of Complex Networks Complex: (Latin = with + fold/weave (com + plex)) Properties of Complex Networks Adjective Modelling Complex ◮ Made up of multiple parts; intricate or detailed. Networks Nutshell ◮ Not simple or straightforward. References Frame 6/61
net • work |ˈnetˌwərk| Overview noun 1 an arrangement of intersecting horizontal and vertical lines. Class admin • a complex system of roads, railroads, or other transportation routes : a network of railroads. Basic definitions 2 a group or system of interconnected people or things : a trade network. Popularity • a group of people who exchange information, contacts, and Examples of experience for professional or social purposes : a support network. Complex Networks • a group of broadcasting stations that connect for the simultaneous Properties of broadcast of a program : the introduction of a second TV network | [as adj. ] Complex Networks network television. Modelling Complex Networks • a number of interconnected computers, machines, or operations : specialized computers that manage multiple outside connections to a network | a Nutshell local cellular phone network. References • a system of connected electrical conductors. 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
Overview Thesaurus deliciousness: Class admin Basic definitions Popularity network Examples of Complex Networks noun Properties of Complex Networks 1 a network of arteries WEB , lattice, net, matrix, mesh, Modelling Complex Networks crisscross, grid, reticulum, reticulation; Anatomy plexus. Nutshell 2 a network of lanes MAZE , labyrinth, warren, tangle. References 3 a network of friends SYSTEM , complex, nexus, web, webwork. Frame 8/61
Overview Ancestry: Class admin Basic definitions From Keith Briggs’s excellent Popularity etymological investigation: ( ⊞ ) Examples of Complex Networks Properties of Complex Networks Modelling Complex Networks Nutshell ◮ Opus reticulatum: References ◮ A Latin origin? [http://serialconsign.com/2007/11/we-put-net-network] Frame 9/61
Overview Ancestry: Class admin Basic definitions First known use: Geneva Bible, 1560 Popularity ‘And thou shalt make unto it a grate like networke of Examples of Complex Networks brass (Exodus xxvii 4).’ Properties of Complex Networks From the OED via Briggs: Modelling Complex Networks ◮ 1658–: reticulate structures in animals Nutshell References ◮ 1839–: rivers and canals ◮ 1869–: railways ◮ 1883–: distribution network of electrical cables ◮ 1914–: wireless broadcasting networks Frame 10/61
Overview Ancestry: Class admin Net and Work are venerable old words: Basic definitions ◮ ‘Net’ first used to mean spider web (King Ælfréd, 888) . Popularity ◮ ‘Work’ appears to have long meant purposeful action. Examples of Complex Networks Properties of Complex Networks Modelling Complex Networks Nutshell References ◮ ‘Network’ = something built based on the idea of natural, flexible lattice or web. ◮ c.f., ironwork, stonework, fretwork. Frame 11/61
Overview Key Observation: ◮ Many complex systems Class admin can be viewed as complex networks Basic definitions Popularity of physical or abstract interactions. Examples of ◮ Opens door to mathematical and numerical analysis. Complex Networks ◮ Dominant approach of last decade of a Properties of Complex Networks theoretical-physics/stat-mechish flavor. Modelling Complex Networks ◮ Mindboggling amount of work published on complex Nutshell networks since 1998... References ◮ ... largely due to your typical theoretical physicist: ◮ Piranha physicus ◮ Hunt in packs. ◮ Feast on new and interesting ideas (see chaos, cellular automata, ...) Frame 12/61
Overview Popularity (according to ISI) Class admin “Collective dynamics of ‘small-world’ networks” [21] Basic definitions Popularity ◮ Watts and Strogatz Examples of Complex Networks Nature, 1998 Properties of ◮ ≈ 4100 citations (as of January 18, 2010) Complex Networks Modelling Complex ◮ Over 1100 citations in 2008 alone. Networks Nutshell “Emergence of scaling in random networks” [2] References ◮ Barabási and Albert Science, 1999 ◮ ≈ 4400 citations (as of January 18, 2010) ◮ Over 1100 citations in 2008 alone. Frame 13/61
Overview Popularity according to books: Class admin Basic definitions Popularity Examples of The Tipping Point: How Little Things can Complex Networks make a Big Difference—Malcolm Gladwell [9] Properties of Complex Networks Modelling Complex Networks Nutshell References Nexus: Small Worlds and the Groundbreaking Science of Networks—Mark Buchanan Frame 14/61
Overview Popularity according to books: Class admin Basic definitions Popularity Linked: How Everything Is Connected to Examples of Complex Networks Everything Else and What It Properties of Means—Albert-Laszlo Barabási Complex Networks Modelling Complex Networks Nutshell References Six Degrees: The Science of a Connected Age—Duncan Watts [19] Frame 15/61
Overview Numerous others: ◮ Complex Social Networks—F. Vega-Redondo [18] Class admin ◮ Fractal River Basins: Chance and Self-Organization—I. Basic definitions Rodríguez-Iturbe and A. Rinaldo [15] Popularity Examples of ◮ Random Graph Dynamics—R. Durette Complex Networks Properties of ◮ Scale-Free Networks—Guido Caldarelli Complex Networks Modelling Complex ◮ Evolution and Structure of the Internet: A Statistical Networks Physics Approach—Romu Pastor-Satorras and Nutshell Alessandro Vespignani References ◮ Complex Graphs and Networks—Fan Chung ◮ Social Network Analysis—Stanley Wasserman and 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 16/61 Mendes [8]
Overview More observations Class admin ◮ But surely networks aren’t new... Basic definitions ◮ Graph theory is well established... Popularity Examples of ◮ Study of social networks started in the 1930’s... Complex Networks ◮ So why all this ‘new’ research on networks? Properties of Complex Networks ◮ Answer: Oodles of Easily Accessible Data. Modelling Complex Networks ◮ We can now inform (alas) our theories Nutshell with a much more measurable reality. ∗ References ◮ Real networks occupy a tiny, low entropy part of all network space and require specific attention. ◮ A worthy goal: establish mechanistic explanations. ◮ What kinds of dynamics lead to these real networks? ∗ If this is upsetting, maybe string theory is for you... Frame 17/61
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