CNT 5805: Network Science Fall 2016 Mainak Chatterjee

The slides that I will be using for this class have been copied from open sources from the Web. I do not claim any intellectual property for the following material. I thank all other instructors for making the slides available and making my life easy. Disclaimers

Some real networks – Social Networks 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 – Information Networks Citation network (directed acyclic) The Web (directed) Peer-to-Peer networks Software graphs – Distribution Networks The Internet (router level, AS level) Power Grids, Telephone Networks Airline networks Transportation Networks (roads, railways, pedestrian traffic)

Some real networks…. – Biological Networks Protein-Protein Interaction Networks Gene regulation networks Gene co-expression networks Metabolic pathways The Food Web Neural Networks – Economic Networks Bank networks Credit card – Natural Networks River networks Leaf networks Epidemic

How do networks “look” like? Let’s look at some pictures… These will give you some idea of what we are dealing with. A word of caution – When was the data collected – How was the data collected (methodology) – Credibility of the experiments Nevertheless, the pictures tell a story

Terrorist Network

Actors (

Links among blogs (2004 presidential) election)

Product recommendations

Facebook The “Social Graph” behind Facebook

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

PoP-level Internet2 network

The Internet at AS level

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

Routers

Power networks

transportation networks: airlines Source: Northwest Airlines WorldTraveler Magazine

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

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

Citric acid cycle Metabolites participate in chemical reactions metabolic networks

Biochemical pathways (Roche) Source: Roche Applied Science,

Gene regulatory networks GRN is a collection of DNA segments in a cell which interact with other indirectly (through their RNA and protein expression products) and with other substances in the cell, thereby governing the expressions levels of Messenger RNA (mRMA) and proteins. 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:

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

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

The Protein Network of Drosophila (a small fly) CuraGen Corporation Science, 2003

KEGG database: Metabolic networks

C. elegans neurons

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

Freshwater food web by Neo Martinez and Richard Williams

Protein interaction networks

Ecological networks

Brain networks

Structural brain connectivity

Economic networks

World-trade networks

exchanges in a company

Phone calls in a country

Socio-epidemic networks

Epidemic networks

River networks

Leaf networks

Nodes: Links: Companies Investment Pharma Research Labs Public Biotechnology Collaborations Financial R&D Network Science: Introduction 2012 Business ties in bio-tech industry

Network Science: Introduction 2012 What message did the pictures convey? Enough of pictures

Network Science: Introduction 2012 We are surrounded by complex systems, from the society (a collection of 7 billion individuals, to communications systems, to neurons in the brain. All these systems work together in a seamless fashion. These systems, random looking at first, upon close inspection display endless signatures of order and self-organization whose quantification, understanding, prediction and eventually control is the major intellectual challenge. Bottomline….it’s the complexity

THE ROLE OF NETWORKS Behind each complex system there is a network (a wiring diagram), that defines the interactions between the component. We will never understand complex system unless we map out and understand the networks behind them. Network Science: Introduction 2012

“Complex” networks 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,...

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

What is Network Science? The study of complex systems that can be represented as (typically dynamic) networks –Society, Economy –Various biological networks (e.g., metabolism) –Brain –WWW, Internet, Transportation nets –Natural networks (global climate system) –Many others Relies on: –Network data (strong empirical basis) –Network models –Network algorithms –Statistics of network data

Main components of Network Science Structural properties of complex networks –E.g., scale-free, small-world Dynamics of networks Dynamics on networks Dynamics of & on networks (co-evolutionary networks) How does structure affect dynamics? And how do dynamics affect structure?

The roots of Network Science Graph Theory Statistical Mechanics Nonlinear Dynamics Games and Learning Data mining (“graph mining”) and machine learning Algorithms Complexity theory

Applications of Network Science Social networks and social media Economic networks Biology Ecology Network medicine Climate science Brain Science and Neuroscience Web Internet and computer networks.. many others

Why study Network Science now? Network Science: Introduction 2012 The list of chemical reactions that take place in a cell were discovered over a 150 year period by biochemists and biologists. In the 1990s they were collected in central databases, offering the first chance to assemble the networks behind a cell. The list of actors that play in each movie were traditionally scattered in books and encyclopedias. With the advent of the Internet, these disparate data were assembled into a central database by imdb.com, mainly to feed the curiosity of movie aficionados. The database offered the first chance for network scientists to explore the structure of the affiliation network behind Hollywood. The detailed list of authors of millions of research papers were traditionally scattered in the table of content of thousands of journals, but recently the Web of Science, Google Scholar, and other sites assembled them into comprehensive databases, easing the search for scientific information. These databases turned into the first science collaboration maps.

Data Availability: Universality: The (urgent) need to understand complexity: THE EMERGENCE OF NETWORK SCIENCE Movie Actor Network, 1998; World Wide Web, C elegans neural wiring diagram 1990 Citation Network, 1998 Metabolic Network, 2000; The architecture of networks emerging in various domains of science, nature, and technology are more similar to each other than one would have expected. During the past decade some of the most important advances towards understanding complexity were provided in context of network theory. Network Science: Introduction 2012

Interdisciplinary: Cell biologists/Computer Scientists/others needs the wiring diagram behind their system, extracting information from incomplete and noisy data sets. Empirical, Data driven: Focus is on data and its utility. Not just mathematical models, but tools to test real data. The value addition will be judged by the insights it offers. Quantitative and Mathematical Nature: Graph theory; organizing principles from statistical physics, control and information theory, statistics and data mining. Computational Intensive: Size of networks giving rise to Big Data. Needs algorithms, database management, data mining, analytics, software tools. THE CHARACTERISTICS OF NETWORK SCIENCE Network Science: Introduction 2012

Impact of Network Science

How come we see relevant ads when we browse? All rely on networks – connections that we have with products/ people/things/etc. ECONOMIC IMPACT – Business exploiting user data Network Science: Introduction 2012

In September 2010 the National Institutes of Health awarded $40 million to researchers at Harvard, Washington University in St. Louis, the University of Minnesota and UCLA, to develop the technologies that could systematically map out brain circuits. The Human Connectome Project (HCP) with the ambitious goal to construct a map of the complete structural and functional neural connections in vivo within and across individuals. BRAIN RESEARCH Network Science: Introduction 2012

If you were to understand the spread of diseases, can you do it without networks? If you were to understand the WWW structure, searchability, etc, hopeless without invoking the Web’s topology. If you want to understand human diseases, it is hopeless without considering the wiring diagram of the cell. MOST IMPORTANT Networks Really Matter Network Science: Introduction 2012

Course Logistics CNT 5805: Network Science Relatively new: Very few universities offer Network Science

Course Website The course website: Linked from my “Teaching” page Instructor: Mainak Chatterjee Office: HEC 305 Office hours: Mon/Wed 4:30 – 6:00 PM or by appointments TA: None (Do NOT use the webcourse

Books A. Barabasi, Network Science / M.E.J. Newman, Networks: An Introduction, Oxford University Press, Not available online. D. Easley and J. Kleinberg, Networks, Crowds and Markets, Cambridge Univ Press,

Topics to be covered…this is what I intend to teach Graph definitions, paths, components, degree distribution, clustering, degree correlations, centrality metrics, small-world property, scale-free property, heavy-tailed degree distributions, network motifs, Poisson networks, Watts-Strogatz model, preferential attachment and its variants, applications in communications and social networks, community identification and detection algorithms, percolation, vulnerabilities, resilience to random and targeted attacks, epidemics, immunization strategies, influence identification, games on networks, strategic network formation, evolution due to cooperation and non-cooperation on social networks.

Grading 4 Assignments (4 X 15) = 60 Points These will be programming assignments and analytical questions. 1 Mid-term exam = 20 points 1 Final exam = 20 points 90+  A 80+  B 70+  C Plus/minus will be used.

Helps if you know (I would do all the basics) Graph Theory –Basic definitions and properties Probability theory –Distribution functions (Binomial, Poisson) Linear Algebra –Eigenvalues and eigenvectors A bit of differential equations Programming knowledge is a must (any language)