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

Overview of Overview of Complex Networks Complex Networks Overview of Complex Networks Principles of Complex Systems Basic definitions Basic definitions Examples of Examples of CSYS/MATH 300, Spring, 2013 | #SpringPoCS2013 Complex Networks Thesaurus deliciousness: Complex Networks Properties of Properties of network Complex Networks Complex Networks Prof. Peter Dodds Nutshell Nutshell noun References References @peterdodds 1 a network of arteries WEB , lattice, net, matrix, mesh, crisscross, grid, reticulum, reticulation; Anatomy plexus. Department of Mathematics & Statistics | Center for Complex Systems | 2 a network of lanes MAZE , labyrinth, warren, tangle. Vermont Advanced Computing Center | University of Vermont 3 a network of friends SYSTEM , complex, nexus, web, webwork. Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License . 1 of 49 4 of 49 Overview of Overview of Outline Ancestry: Complex Networks Complex Networks Basic definitions Basic definitions Examples of Examples of Complex Networks Complex Networks Basic definitions From Keith Briggs’s excellent etymological Properties of Properties of investigation: ( ⊞ ) Complex Networks Complex Networks Nutshell Nutshell Examples of Complex Networks References References Properties of Complex Networks ◮ Opus reticulatum: ◮ A Latin origin? Nutshell References [http://serialconsign.com/2007/11/we-put-net-network] 2 of 49 5 of 49 Overview of Ancestry: Overview of net • work |ˈnetˌwərk| 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 : Examples of Examples of a network of railroads. Complex Networks Complex Networks First known use: Geneva Bible, 1560 2 a group or system of interconnected people or things : a trade network. Properties of Properties of • a group of people who exchange information, contacts, and Complex Networks ‘And thou shalt make unto it a grate like networke of Complex Networks experience for professional or social purposes : a support network. Nutshell brass (Exodus xxvii 4).’ Nutshell • a group of broadcasting stations that connect for the simultaneous References References broadcast of a program : the introduction of a second TV network | [as adj. ] network television. From the OED via Briggs: • a number of interconnected computers, machines, or operations : ◮ 1658–: reticulate structures in animals specialized computers that manage multiple outside connections to a network | a local cellular phone network. ◮ 1839–: rivers and canals • a system of connected electrical conductors. ◮ 1869–: railways verb [ trans. ] ◮ 1883–: distribution network of electrical cables connect as or operate with a network : the stock exchanges have proven to be resourceful in networking these deals. ◮ 1914–: wireless broadcasting networks • 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. 3 of 49 6 of 49

Overview of Overview of Ancestry: Popularity (according to Google Scholar) 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” [3] References References Times cited: 3,500 (as of March 18, 2013) ◮ M. Newman “The structure and function of complex networks” [13] Times cited: 9,100 (as of March 18, 2013) ◮ R. Albert and A.-L. Barabási “Statistical mechanics of complex networks” [1] Times cited: 11,600 (as of March 18, 2013) ◮ ‘Network’ = something built based on the idea of natural, flexible lattice or web. ◮ c.f., ironwork, stonework, fretwork. 7 of 49 10 of 49 Overview of Overview of Key Observation: Popularity according to textbooks: 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 Complex Networks Complex Networks ◮ Opens door to mathematical and numerical analysis. Textbooks: Nutshell Nutshell ◮ Dominant approach of last decade of a ◮ Mark Newman (Physics, Michigan) References References theoretical-physics/stat-mechish flavor. “Networks: An Introduction” ( ⊞ ) ◮ Mindboggling amount of work published on complex ◮ David Easley and Jon Kleinberg (Economics and Computer Science, Cornell) networks since 1998... “Networks, Crowds, and Markets: Reasoning About a ◮ ... largely due to your typical theoretical physicist: Highly Connected World” ( ⊞ ) ◮ Piranha physicus ◮ Hunt in packs. ◮ Feast on new and interesting ideas (see chaos, cellular automata, ...) 8 of 49 11 of 49 Popularity (according to Google Scholar) Overview of Popularity according to books: Overview of Complex Networks Complex Networks Basic definitions Basic definitions Examples of Examples of Complex Networks Complex Networks “Collective dynamics of ‘small-world’ networks” [18] Properties of Properties of Complex Networks The Tipping Point: How Little Things can Complex Networks ◮ Watts and Strogatz make a Big Difference—Malcolm Gladwell [8] Nutshell Nutshell Nature, 1998 References References ◮ Cited ≈ 18 , 450 times (as of March 18, 2013) “Emergence of scaling in random networks” [2] ◮ Barabási and Albert Nexus: Small Worlds and the Groundbreaking Science, 1999 Science of Networks—Mark Buchanan ◮ Cited ≈ 16 , 050 times (as of March 18, 2013) 9 of 49 12 of 49

Overview of Overview of Popularity according to books: More observations Complex Networks Complex Networks Basic definitions Basic definitions ◮ Web-scale data sets can be overly exciting. Examples of Examples of Complex Networks Complex Networks Properties of Properties of Linked: How Everything Is Connected to Witness: Complex Networks Complex Networks Everything Else and What It Nutshell Nutshell ◮ The End of Theory: The Data Deluge Makes the Means—Albert-Laszlo Barabási References References Scientific Theory Obsolete (Anderson, Wired) ( ⊞ ) ◮ “The Unreasonable Effectiveness of Data,” Halevy et al. [9] . ◮ c.f. Wigner’s “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” [19] Six Degrees: The Science of a Connected Age—Duncan Watts [17] But: ◮ For scientists, description is only part of the battle. ◮ We still need to understand. 13 of 49 16 of 49 Overview of Overview of Super Basic definitions Numerous others . . . Complex Networks Complex Networks ◮ Complex Social Networks—F . Vega-Redondo [16] 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 [14] Nodes = A collection of entities which have Properties of Properties of Complex Networks Complex Networks ◮ Random Graph Dynamics—R. Durette properties that are somehow related to each other Nutshell Nutshell ◮ Scale-Free Networks—Guido Caldarelli ◮ e.g., people, forks in rivers, proteins, webpages, References References organisms,... ◮ Evolution and Structure of the Internet: A Statistical Physics Approach—Romu Pastor-Satorras and Alessandro Vespignani Links = Connections between nodes ◮ Links may be directed or undirected. ◮ Complex Graphs and Networks—Fan Chung ◮ Links may be binary or weighted. ◮ Social Network Analysis—Stanley Wasserman and Kathleen Faust Other spiffing words: vertices and edges. ◮ Handbook of Graphs and Networks—Eds: Stefan Bornholdt and H. G. Schuster [5] ◮ Evolution of Networks—S. N. Dorogovtsev and J. F . F . Mendes [7] 14 of 49 17 of 49 More observations Overview of Super Basic definitions Overview of Complex Networks Complex Networks Basic definitions Basic definitions Examples of Examples of Complex Networks Complex Networks Node degree = Number of links per node ◮ But surely networks aren’t new... Properties of Properties of Complex Networks Complex Networks ◮ Notation: Node i ’s degree = k i . ◮ Graph theory is well established... Nutshell Nutshell ◮ k i = 0,1,2,. . . . ◮ Study of social networks started in the 1930’s... References References ◮ Notation: the average degree of a network = � k � ◮ So why all this ‘new’ research on networks? (and sometimes z ) ◮ Answer: Oodles of Easily Accessible Data. ◮ Connection between number of edges m and ◮ We can now inform (alas) our theories average degree: with a much more measurable reality. ∗ � k � = 2 m N . ◮ A worthy goal: establish mechanistic explanations. ∗ If this is upsetting, maybe string theory is for you... ◮ Defn: N i = the set of i ’s k i neighbors 15 of 49 18 of 49