Complex Networks :. .: Lectures notes for Basics of Complex - - PowerPoint PPT Presentation

Complex Networks :. .: Lectures notes for Basics of Complex Networks Course 295C Fall, 2007 University of Vermont

• Prof. Peter S. Dodds

Basics of Complex Systems 1/14

Complex Networks :. .: Observation Complex systems comprise many interacting parts. ❑❡② ♦❜s❡r✈❛t✐♦♥✿ ■♥t❡r❛❝t✐♦♥ ♣❛tt❡r♥s ❝❛♥ ❜❡ r❡♣r❡s❡♥t❡❞ ❛s ❛ ♥❡t✇♦r❦✳

Basics of Complex Systems 2/14

Complex Networks :. .: Observation Complex systems comprise many interacting parts. Key observation: Interaction patterns can be represented as a network.

Basics of Complex Systems 3/14

Complex Networks :. .: Definitions Network: (net + work, 1500’s) Noun: 1. Any interconnected group or system

• 2. Multiple computers and other devices connected together to

share information. Verb: 1. To interact socially for the purpose of getting connections or personal advancement

• 2. To connect two or more computers or other computerized

devices

Basics of Complex Systems 4/14

Complex Networks :. .: Definitions Nodes: A collection of entities which have properties that are somehow related to each other. e.g., people, forks in rivers, proteins, webpages, organisms,...

Basics of Complex Systems 5/14

Complex Networks :. .: Definitions Links are connections between nodes. ▲✐♥❦s ♠❛② ❜❡ r❡❛❧ ❛♥❞ ☞①❡❞ ✭r✐✈❡rs✮✱ r❡❛❧ ❛♥❞ ❞②♥❛♠✐❝ ✭❛✐r❧✐♥❡ r♦✉t❡s✮✱ ❝♦♥♥❡❝t ❝❧❛ss❡s ♦❢ ❛❣❡♥ts ✭❢♦♦❞ ✇❡❜s✮✱ ❛❜str❛❝t ✇✐t❤ r❡❛❧ ✐♠♣❛❝t ✭❤②♣❡r❧✐♥❦s✮✱ ♦r ♠❡r❡❧② ❛❜st❛❝t ✭s❡♠❛♥t✐❝ ❝♦♥♥❡❝t✐♦♥s ❜❡t✇❡❡♥ ❝♦♥❝❡♣ts✮✳ ▲✐♥❦s ♠❛② ❜❡ ❞✐r❡❝t❡❞ ♦r ✉♥❞✐r❡❝t❡❞✳ ▲✐♥❦s ♠❛② ❜❡ ❜✐♥❛r② ♦r ✇❡✐❣❤t❡❞✳

Basics of Complex Systems 6/14

Complex Networks :. .: Definitions Links are connections between nodes. Links may be real and fixed (rivers), real and dynamic (airline routes), connect classes of agents (food webs), abstract with real impact (hyperlinks), or merely abstact (semantic connections between concepts). ▲✐♥❦s ♠❛② ❜❡ ❞✐r❡❝t❡❞ ♦r ✉♥❞✐r❡❝t❡❞✳ ▲✐♥❦s ♠❛② ❜❡ ❜✐♥❛r② ♦r ✇❡✐❣❤t❡❞✳

Basics of Complex Systems 7/14

Complex Networks :. .: Definitions Links are connections between nodes. Links may be real and fixed (rivers), real and dynamic (airline routes), connect classes of agents (food webs), abstract with real impact (hyperlinks), or merely abstact (semantic connections between concepts). Links may be directed or undirected. ▲✐♥❦s ♠❛② ❜❡ ❜✐♥❛r② ♦r ✇❡✐❣❤t❡❞✳

Basics of Complex Systems 8/14

Complex Networks :. .: Definitions Links are connections between nodes. Links may be real and fixed (rivers), real and dynamic (airline routes), connect classes of agents (food webs), abstract with real impact (hyperlinks), or merely abstact (semantic connections between concepts). Links may be directed or undirected. Links may be binary or weighted.

Basics of Complex Systems 9/14

Complex Networks :. .: Definitions Node degree: Number of links per node. Notation: Node i’s degree = ki. ki = 0,1,2,. . . .

Basics of Complex Systems 10/14

Complex Networks :. .: Examples

Physical networks

➤ River networks ➤ Trees and leaves ➤ Blood networks ➤ Neural networks ➤ The Internet ➤ Road networks ➤ Power grids

(opte.com)

Distribution (branching) versus redistribution (cyclical)

Basics of Complex Systems 11/14

Complex Networks :. .: Examples

Interaction networks

➤ Biochemical networks ➤ Gene-protein networks ➤ Food webs: who eats whom ➤ The World Wide Web (?) ➤ Airline networks ➤ The Blogosphere ➤ Call networks (AT&T) ➤ The Media

(datamining.typepad.com) Basics of Complex Systems 12/14

Complex Networks :. .: Examples

Interaction networks

Social networks: ➤ Kinship ➤ Friends ➤ Acquaintances ➤ Boards and directors ➤ Organizations ➤ myspace.com, facebook.com

(Bearman et al., 2004)

‘Remotely sensed’ by: email activity, instant messaging, phone logs (*cough*).

Basics of Complex Systems 13/14

Complex Networks :. .: Examples

Relational networks

➤ Consumer purchases (Wal-Mart: ≈ 4 petabyte = 4 × 1015 bytes) ➤ Thesauri: Networks of words generated by meanings ➤ Knowledge/Databases/Ideas ➤ Metadata—Tagging: del.icio.us flickr.com shadows.com

common tags cloud | list

community daily dictionary education encyclopedia english free imported info information internet knowledge learning news reference research resource resources search tools useful web web2.0 wiki

wikipedia Basics of Complex Systems 14/14