PoCS | @pocsvox Overview of Overview of Complex Networks Complex Networks Principles of Complex Systems | @pocsvox Basic definitions CSYS/MATH 300, Fall, 2013 | #FallPoCS2013 Examples of Complex Networks Properties of Complex Networks Prof. Peter Dodds | @peterdodds Nutshell References Dept. of Mathematics & Statistics | Vermont Complex Systems Center Vermont Advanced Computing Core | University of Vermont P What’s o The C Story? S P What’s o The C Story? S Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License . 1 of 52
PoCS | @pocsvox These slides are brought to you by: Overview of Complex Networks Basic definitions Examples of Complex Networks Properties of Complex Networks Nutshell References P What’s o The C Story? S 2 of 52
PoCS | @pocsvox Outline Overview of Complex Networks Basic definitions Basic definitions Examples of Complex Networks Properties of Complex Networks Examples of Complex Networks Nutshell References Properties of Complex Networks Nutshell P What’s o References The C Story? S 3 of 52
PoCS | @pocsvox net • work |ˈnetˌwərk| Overview of Complex Networks noun 1 an arrangement of intersecting horizontal and vertical lines. • a complex system of roads, railroads, or other transportation routes : Basic definitions a network of railroads. Examples of 2 a group or system of interconnected people or things : a trade network. Complex Networks • a group of people who exchange information, contacts, and Properties of experience for professional or social purposes : a support network. Complex Networks • a group of broadcasting stations that connect for the simultaneous Nutshell broadcast of a program : the introduction of a second TV network | [as adj. ] References network television. • a number of interconnected computers, machines, or operations : specialized computers that manage multiple outside connections to a network | a local cellular phone network. • 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. P What’s o • link (machines, esp. computers) to operate interactively : [as adj. ] ( The C Story? S 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. 4 of 52
PoCS | @pocsvox Overview of Complex Networks Basic definitions Thesaurus deliciousness: Examples of Complex Networks network Properties of Complex Networks noun Nutshell 1 a network of arteries WEB , lattice, net, matrix, mesh, References crisscross, grid, reticulum, reticulation; Anatomy plexus. 2 a network of lanes MAZE , labyrinth, warren, tangle. 3 a network of friends SYSTEM , complex, nexus, web, webwork. P What’s o The C Story? S 5 of 52
PoCS | @pocsvox Ancestry: Overview of Complex Networks Basic definitions From Keith Briggs’s excellent etymological Examples of Complex Networks investigation: ( ⊞ ) Properties of Complex Networks Nutshell References ◮ Opus reticulatum: ◮ A Latin origin? P What’s o [http://serialconsign.com/2007/11/we-put-net-network] The C Story? S 6 of 52
PoCS | @pocsvox Ancestry: Overview of Complex Networks Basic definitions First known use: Geneva Bible, 1560 Examples of Complex Networks ‘And thou shalt make unto it a grate like networke of Properties of Complex Networks brass (Exodus xxvii 4).’ Nutshell References From the OED via Briggs: ◮ 1658–: reticulate structures in animals ◮ 1839–: rivers and canals ◮ 1869–: railways ◮ 1883–: distribution network of electrical cables P What’s ◮ 1914–: wireless broadcasting networks o The C Story? S 7 of 52
PoCS | @pocsvox Ancestry: Overview of Complex Networks Net and Work are venerable old words: Basic definitions ◮ ‘Net’ first used to mean spider web (King Ælfréd, 888) . Examples of Complex Networks ◮ ‘Work’ appear to have long meant purposeful action. Properties of Complex Networks Nutshell References P ◮ ‘Network’ = something built based on the idea of What’s o The C Story? natural, flexible lattice or web. S ◮ c.f., ironwork, stonework, fretwork. 8 of 52
PoCS | @pocsvox Key Observation: Overview of Complex Networks ◮ Many complex systems Basic definitions can be viewed as complex networks Examples of of physical or abstract interactions. Complex Networks ◮ Opens door to mathematical and numerical analysis. Properties of Complex Networks ◮ Dominant approach of last decade of a Nutshell theoretical-physics/stat-mechish flavor. References ◮ Mindboggling amount of work published on complex networks since 1998... ◮ ... largely due to your typical theoretical physicist: ◮ Piranha physicus P What’s o The C ◮ Hunt in packs. Story? S ◮ Feast on new and interesting ideas (see chaos, cellular automata, ...) 9 of 52
PoCS | @pocsvox Popularity (according to Google Scholar) Overview of Complex Networks Basic definitions Examples of “Collective dynamics of ‘small-world’ networks” [18] Complex Networks Properties of Duncan Watts and Steve Strogatz Complex Networks Nature, 1998 Nutshell References Times cited: ∼ 20 , 500 ( ⊞ ) (as of September 30, 2013) “Emergence of scaling in random networks” [2] László Barabási and Réka Albert Science, 1999 Times cited: ∼ 17 , 925 ( ⊞ ) (as of September 30, 2013) P What’s o The C Story? S 10 of 52
PoCS | @pocsvox Popularity (according to Google Scholar) Overview of Complex Networks Review articles: Basic definitions Examples of ◮ S. Boccaletti et al., Complex Networks Physics Reports, 2006, Properties of Complex Networks “Complex networks: structure and dynamics” [3] Nutshell Times cited: ∼ 4,500 ( ⊞ ) (as of September 30, 2013) References ◮ M. Newman, SIAM Review, 2003, “The structure and function of complex networks” [13] Times cited: ∼ 10,050 ( ⊞ ) (as of September 30, 2013) ◮ R. Albert and A.-L. Barabási Reviews of Modern Physics, 2002, P What’s o “Statistical mechanics of complex networks” [1] The C Story? S Times cited: ∼ 12,670 ( ⊞ ) (as of September 30, 2013) 11 of 52
PoCS | @pocsvox Popularity according to textbooks: Overview of Complex Networks Basic definitions Examples of Complex Networks Properties of Textbooks: Complex Networks ◮ Mark Newman (Physics, Michigan) Nutshell References “Networks: An Introduction” ( ⊞ ) ◮ David Easley and Jon Kleinberg (Economics and Computer Science, Cornell) “Networks, Crowds, and Markets: Reasoning About a Highly Connected World” ( ⊞ ) P What’s o The C Story? S 12 of 52
PoCS | @pocsvox Popularity according to books: Overview of Complex Networks Basic definitions Examples of Complex Networks The Tipping Point: How Little Things can Properties of Complex Networks make a Big Difference—Malcolm Gladwell [8] Nutshell References Nexus: Small Worlds and the Groundbreaking Science of Networks—Mark Buchanan P What’s o The C Story? S 13 of 52
PoCS | @pocsvox Popularity according to books: Overview of Complex Networks Basic definitions Examples of Complex Networks Linked: How Everything Is Connected to Properties of Everything Else and What It Complex Networks Means—Albert-Laszlo Barabási Nutshell References Six Degrees: The Science of a Connected Age—Duncan Watts [17] P What’s o The C Story? S 14 of 52
PoCS | @pocsvox Numerous others . . . Overview of Complex Networks ◮ Complex Social Networks—F. Vega-Redondo [16] ◮ Fractal River Basins: Chance and Self-Organization—I. Basic definitions Rodríguez-Iturbe and A. Rinaldo [14] Examples of Complex Networks ◮ Random Graph Dynamics—R. Durette Properties of Complex Networks ◮ Scale-Free Networks—Guido Caldarelli Nutshell References ◮ Evolution and Structure of the Internet: A Statistical Physics Approach—Romu Pastor-Satorras and Alessandro Vespignani ◮ Complex Graphs and Networks—Fan Chung ◮ Social Network Analysis—Stanley Wasserman and Kathleen Faust P What’s o ◮ Handbook of Graphs and Networks—Eds: Stefan The C Story? S Bornholdt and H. G. Schuster [5] ◮ Evolution of Networks—S. N. Dorogovtsev and J. F . F . Mendes [7] 15 of 52
PoCS | @pocsvox More observations Overview of Complex Networks Basic definitions Examples of ◮ But surely networks aren’t new... Complex Networks ◮ Graph theory is well established... Properties of Complex Networks ◮ Study of social networks started in the 1930’s... Nutshell References ◮ So why all this ‘new’ research on networks? ◮ Answer: Oodles of Easily Accessible Data. ◮ We can now inform (alas) our theories with a much more measurable reality. ∗ ◮ A worthy goal: establish mechanistic explanations. ∗ If this is upsetting, maybe string theory is for you... P What’s o The C Story? S 16 of 52
Recommend
More recommend
