Lecture 1: Introduction CS 790g: Complex Networks Slides are modified from Statistical physics of complex networks by Sergei Maslov and Complex Adaptive Systems by Eileen Kraemer

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 2

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. 3

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 4

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... 5

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 6

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.  The specificity of network nodes and links can be quantitatively characterized by weights Vertex-WeightedEdge-Weighted  7

Networks As Graphs - 2 Networks having no cycles are termed trees. The more cycles the network has, the more complex it is. A network can be connected (presented by a single component) or disconnected (presented by several disjoint components). connecteddisconnected trees cyclic graphs 8

Networks As Graphs - 3 Some Basic Types of Graphs Paths Stars Cycles Complete Graphs Bipartite Graphs 9

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 10

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 11

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) 12

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

Networks in complex systems Complex systems Large number of components interacting with each other All components and/or interactions are different from each other Paradigms: 10 4 types of proteins in an organism, 10 6 routers in the Internet 10 9 web pages in the WWW 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 14

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 15

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). 16

Social Networks Links denote a social interaction Networks of acquaintances collaboration networks actor networks co-authorship networks director networks phone-call networks networks IM networks Bluetooth networks sexual networks home page/blog networks 17

Network of actor co-starring in movies 18

Actors 19

Networks of scientists’ co-authorship of papers 20

Scientists 21

boards of directors Source: 22

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) 23

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,

“Six degrees of Mohammed Atta” Uncloaking Terrorist Networks, by Valdis Krebs terrorist networks 25

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 26

natural language processing Wordnet Source: 27

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

World Wide Web 29

Networks of personal homepages StanfordMIT Source: Lada A. Adamic and Eytan Adar, ‘Friends and neighbors on the web’, Social Networks, 25(3): , July

European University Web Pages 31

HP communication 32

Links among blogs (2004 presidential election) 33

Product recommendations 34

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 35

The Internet at AS level 36

Internet as measured by Hal Burch and Bill Cheswick's Internet Mapping Project.Internet Mapping Project 37

routers 38

Power networks 39

transportation networks: airlines Source: Northwest Airlines WorldTraveler Magazine 40

transportation networks: railway maps Source: TRTA, March Tokyo rail map 41

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 42

Citric acid cycle Metabolites participate in chemical reactions metabolic networks 43

Biochemical pathways (Roche) Source: Roche Applied Science, 44

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: 45

MAPK signalingInhibition of apoptosis Images from ResNet3.0 by Ariadne Genomics 46

protein-gene interactions protein-protein interactions PROTEOME GENOME Citrate Cycle METABOLISM Bio-chemical reactions Bio map by L-A Barabasi _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 47

Protein binding networks Baker’s yeast S. cerevisiae (only nuclear proteins shown) Nematode worm C. elegans 48

Transcription regulatory networks Bacterium: E. coli Single-celled eukaryote: S. cerevisiae 49

The Protein Network of Drosophila CuraGen Corporation Science,

KEGG database: Metabolic networks 51

C. elegans neurons 52

Network of Interacting Pathways (NIP) A.Mazurie D.Bonchev G.A. Buck, organisms 53

Freshwater food web by Neo Martinez and Richard Williams 54

Examples of complex networks: geometric, regular slides from Eileen Kraemer 55

Examples of complex networks: semi-geometric, irregular 56

Elementary features: node diversity and dynamics 57

Elementary features: edge diversity and dynamics 58

Network Questions: Structural 1. How many connections does the average node have? 2. Are some nodes more connected than others? 3. Is the entire network connected? 4. On average, how many links are there between nodes? 5. Are there clusters or groupings within which the connections are particularly strong? 6. What is the best way to characterize a complex network? 7. How can we tell if two networks are “different”? 8. Are there useful ways of classifying or categorizing networks? slides from David P. Feldman 59

Network Questions: Communities 1. Are there clusters or groupings within which the connections are particularly strong? 2. What is the best way to discover communities, especially in large networks? 3. How can we tell if these communities are statistically significant? 4. What do these clusters tell us in specific applications? 60

Network Questions: Dynamics of 1. How can we model the growth of networks? 2. What are the important features of networks that our models should capture? 3. Are there “universal” models of network growth? What details matter and what details don’t? 4. To what extent are these models appropriate null models for statistical inference? 5. What’s the deal with power laws, anyway? 61

Network Questions: Dynamics on 1. How do diseases/computer viruses/innovations/ rumors/revolutions propagate on networks? 2. What properties of networks are relevant to the answer of the above question? 3. If you wanted to prevent (or encourage) spread of something on a network, what should you do? 4. What types of networks are robust to random attack or failure? 5. What types of networks are robust to directed attack? 6. How are dynamics of and dynamics on coupled? 62

Network Questions: Algorithms 1. What types of networks are searchable or navigable? 2. What are good ways to visualize complex networks? 3. How does google page rank work? 4. If the internet were to double in size, would it still work? 63

Network Questions: Algorithms There are also many domain-specific questions: 1. Are networks a sensible way to think about gene regulation or protein interactions or food webs? 2. What can social networks tell us about how people interact and form communities and make friends and enemies? 3. Lots and lots of other theoretical and methodological questions What else can be viewed as a network? Many applications await. 64

Network Questions: Outlook Advances in available data, computing speed, and algorithms have made it possible to apply network analysis to a vast and growing number of phenomena. This means that there is lots of exciting, novel work being done. This work is a mixture of awesome, exploratory, misleading, irrelevant, relevant, fascinating, ground-breaking, important, and just plain wrong. It is relatively easy to fool oneself into seeing thing that aren’t there when analyzing networks. This is the case with almost anything, not just networks. For networks, how can we be more careful and scientific, and not just descriptive and empirical? 65

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 66