and Complex Adaptive Systems by Eileen Kraemer Lecture 2: Introduction CS 765: Complex Networks Slides are modified from Statistical physics of complex networks by Sergei Maslov and Complex Adaptive Systems by Eileen Kraemer

Network: (net + work, 1500’s) Noun: Basic definitions Network: (net + work, 1500’s) Noun: Any interconnected group or system Multiple computers and other devices connected together to share information Verb: To interact socially for the purpose of getting connections or personal advancement To connect two or more computers or other computerized devices slides from Peter Dodds

Links = Connections between nodes Basic 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,... Links = Connections between nodes may be real and fixed (rivers), real and dynamic (airline routes), abstract with physical impact (hyperlinks), purely abstract (semantic connections between concepts). Links may be directed or undirected. Links may be binary or weighted.

Complex: (Latin = with + fold/weave (com + plex)) Adjective Basic definitions Complex: (Latin = with + fold/weave (com + plex)) Adjective Made up of multiple parts; intricate or detailed. Not simple or straightforward Complex System—Basic ingredients: Relationships are nonlinear Relationships contain feedback loops Complex systems are open (out of equilibrium) Modular (nested)/multiscale structure Opaque boundaries May result in emergent phenomena Many complex systems can be regarded as complex networks of physical or abstract interactions Opens door to mathematical and numerical analysis

What passes for a complex network? Complex networks are large (in node number) Complex networks are sparse (low edge to node ratio) Complex networks are usually dynamic and evolving Complex networks can be social, economic, natural, informational, abstract, ... Isn’t this graph theory? Yes, but emphasis is on data and mechanistic explanations...

What is a Network? Network is a mathematical structure composed of points connected by lines Network Theory <-> Graph Theory Network  Graph Nodes  Vertices (points) Links  Edges (Lines) A network can be build for any functional system System vs. Parts = Networks vs. Nodes

Networks As Graphs Networks can be undirected or directed, depending on whether the interaction between two neighboring nodes proceeds in both directions or in only one of them, respectively. 1 2 3 4 5 6  The specificity of network nodes and links can be quantitatively characterized by weights 2.5 7.3 3.3 12.7 8.1 5.4 Vertex-Weighted Edge-Weighted

Networks As Graphs - 2 A network can be connected (presented by a single component) or disconnected (presented by several disjoint components). connected disconnected Networks having no cycles are termed trees. The more cycles the network has, the more complex it is. trees cyclic graphs

Networks As Graphs - 3 Some Basic Types of Graphs Paths Stars Cycles Complete Graphs Bipartite Graphs

Historical perspective on Complex Networks In the beginning.. there was REDUCTIONISM All we need to know is the behavior of the system elements Particles in physics, molecules or proteins in biology, communication links in the Internet Complex systems are nothing but the result of many interactions between the system’s elements No new phenomena will emerge when we consider the entire system A centuries-old very flawed scientific tradition.. slides by Constantine Dovrolis

Historical perspective During the 80’s and early 90’s, several parallel approaches departed from reductionism Consider the entire SYSTEM attempting to understand/ explain its COMPLEXITY B. Mandelbrot and others: Chaos and non-linear dynamical systems (the math of complexity) P. Bak: Self-Organized Criticality – The edge of chaos S. Wolfram: Cellular Automata S. Kauffman: Random Boolean Networks I. Prigogine: Dissipative Structures J. Holland: Emergence H. Maturana, F. Varela: Autopoiesis networks & cognition Systems Biology

Historical perspective Systems approach: thinking about Networks The focus moves from the elements (network nodes) to their interactions (network links) To a certain degree, the structural details of each element become less important than the network of interactions Some system properties, such as Robustness, Fragility, Modularity, Hierarchy, Evolvability, Redundancy (and others) can be better understood through the Networks approach Some milestones: 1998: Small-World Networks (D.Watts and S.Strogatz) 1999: Scale-Free Networks (R.Albert & A.L.Barabasi) 2002: Network Motifs (U.Alon)

The evolution of the meaning of protein function traditional view post-genomic view from Eisenberg et al. Nature 2000 405: 823-6

Networks in complex systems Large number of components interacting with each other All components and/or interactions are different from each other Paradigms: 104 types of proteins in an organism, 106 routers in the Internet 109 web pages in the WWW 1011 neurons in a human brain The simplest property: who interacts with whom? can be visualized as a network Complex networks are just a backbone for complex dynamical systems

Why study the topology of Complex Networks? Lots of easily available data Large networks may contain information about basic design principles and/or evolutionary history of the complex system This is similar to paleontology: learning about an animal from its backbone

Early social network analysis 1933 Moreno displays first sociogram at meeting of the Medical Society of the state of New York article in NYT interests: effect of networks on e.g. disease propagation Preceded by studies of (pre)school children in the 1920’s Source: The New York Times (April 3, 1933, page 17).

Links denote a social interaction Social Networks Links denote a social interaction Networks of acquaintances collaboration networks actor networks co-authorship networks director networks phone-call networks e-mail networks IM networks Bluetooth networks sexual networks home page/blog networks

Network of actor co-starring in movies

Actors

Networks of scientists’ co-authorship of papers

Scientists

boards of directors Source: http://theyrule.net

Political/Financial Networks Mark Lombardi: tracked and mapped global financial fiascos in the 1980s and 1990s searched public sources such as news articles drew networks by hand (some drawings as wide as 10ft)

Understanding through visualization “I happened to be in the Drawing Center when the Lombardi show was being installed and several consultants to the Department of Homeland Security came in to take a look. They said they found the work revelatory, not because the financial and political connections he mapped were new to them, but because Lombardi showed them an elegant way to array disparate information and make sense of things, which they thought might be useful to their security efforts. I didn't know whether to find that response comforting or alarming, but I saw exactly what they meant.” Michael Kimmelman Webs Connecting the Power Brokers, the Money and the World NY Times November 14, 2003

terrorist networks “Six degrees of Mohammed Atta” Uncloaking Terrorist Networks, by Valdis Krebs

Knowledge (Information) Networks Nodes store information, links associate information Citation network (directed acyclic) The Web (directed) Peer-to-Peer networks Word networks Networks of Trust Software graphs

natural language processing Wordnet Source: http://wordnet.princeton.edu/man/wnlicens.7WN

online social networks Friendster "Vizster: Visualizing Online Social Networks." Jeffrey Heer and danah boyd. IEEE Symposium on Information Visualization (InfoViz 2005).

World Wide Web

Networks of personal homepages Stanford MIT Source: Lada A. Adamic and Eytan Adar, ‘Friends and neighbors on the web’, Social Networks, 25(3):211-230, July 2003

European University Web Pages

HP e-mail communication

Links among blogs (2004 presidential election)

Product recommendations

Technological networks Networks built for distribution of commodity The Internet router level, AS level Power Grids Airline networks Telephone networks Transportation Networks roads, railways, pedestrian traffic

The Internet at AS level

ASes

Internet as measured by Hal Burch and Bill Cheswick's Internet Mapping Project.

Routers

Power networks

transportation networks: airlines Source: Northwest Airlines WorldTraveler Magazine

transportation networks: railway maps Source: TRTA, March 2003 - Tokyo rail map

Biological systems represented as networks Biological networks Biological systems represented as networks Protein-Protein Interaction Networks Gene regulation networks Gene co-expression networks Metabolic pathways The Food Web Neural Networks

metabolic networks Citric acid cycle Metabolites participate in chemical reactions

Biochemical pathways (Roche) Source: Roche Applied Science, http://www.expasy.org/cgi-bin/show_thumbnails.pl

gene regulatory networks humans have 30,000 genes the complexity is in the interaction of genes can we predict what result of the inhibition of one gene will be? Source: http://www.zaik.uni-koeln.de/bioinformatik/regulatorynets.html.en

Images from ResNet3.0 by Ariadne Genomics Inhibition of apoptosis MAPK signaling

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Bio map by L-A Barabasi GENOME protein-gene interactions _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ PROTEOME - - protein-protein interactions Citrate Cycle METABOLISM Bio-chemical reactions

Protein binding networks Baker’s yeast S. cerevisiae (only nuclear proteins shown) Nematode worm C. elegans

Transcription regulatory networks Single-celled eukaryote: S. cerevisiae Bacterium: E. coli

The Protein Network of Drosophila CuraGen Corporation Science, 2003

Metabolic networks KEGG database: http://www.genome.ad.jp/kegg/kegg2.html

C. elegans neurons

Network of Interacting Pathways (NIP) 381 organisms A.Mazurie D.Bonchev G.A. Buck, 2007

Freshwater food web by Neo Martinez and Richard Williams

Examples of complex networks: geometric, regular slides from Eileen Kraemer

Examples of complex networks: semi-geometric, irregular

Elementary features: node diversity and dynamics

Elementary features: edge diversity and dynamics

Wrap up networks are everywhere and can be used to describe many, many systems by modeling networks we can start to understand their properties and the implications those properties have for processes occurring on the network