Understanding Networks: Analyzing Connections in Diverse Systems

1. MIS 644 Social Network Analysis Chapter 1 Introduction 2014/2015 Fall

2. Outline Networks Why to study networks Examples of networks Properties of networks Outline of the course

3. Networks • Collection of objects in which some pairs are connected by links • Verticies or nodes actors in SNA • Links adges

4. Why to study networks • Individual parts or components linked by some way • Examples • Internet: collection of computers linked by communication links • social networks: people by friendship relations • Individual components • How a computer works • How a humen being feals or acts • Connections or interactions • Communication protocoles • Dynamics of human friendship

5. Third approach (1) • Patterns of connections • Network - simplified reprsentation abstraction • Components - nodes • Connections - links • Patterns of interactions • Affects behavior of systems • Ex: connection patterns – Internet • Affect – routers, efficiency of tranfering data • Ex: in social networks • How people learn, form opinions or gether news • spread of disease • Structure - behavior

6. Third approach (2) • Verious disiplines • Mathematical, comutational, statistical • Analysing, modeling and understanding networks • Many tools – simple network representation • Vertscies and edges • Ex: • Which is the best connected vertex • Length of path from one vertex to another • Network models • Predictions about processes on networks • The way trafic flow over Internet • The way diseases spread through a community

7. Third approach (3) • Not always works • Depens on • what the system is and does • Specific questions to be answered • Networks are • Gneral and powerful • Way of representing • Patterns of connection and interraction of components

8. Examples • Technological networks • Social and economic networks: • Information networks • Biological netwoks

9. Technological Networks • Internet • Electrical power grids • Phone networks • Transport networks: • Roads, airline connection between airports, rail roads and subway networks

10. Internet • Vertecies – computers, rooters • edges – physical data connections • Optical fibers or telephone lines • Nan made, carefully engineered • Its structiure is not known exactly • Many different groups, little centrilized control • See Figure 1.1 of N-N • Why study the network structure of Internet? • How to choose a route? • Is the shortest route fhe fastest? • How to avoid buttlenecks in the trafic flow? • What happens when a vertex or edge fails? • Where to add new capacity • Development of new standards or protocoles

11. Information Networks • Logical connections • www • E-mail • Phone calls • Nodes: telephone number • Directed or weihted links: number of calls from A to B • Trust network • Link: one accepts other public key • Citation

12. Web • Network of information stored in Web pages • Vertcies – web pages • Edges – hyperlinks - software constract • Content structure – link structure • Useful page gets many links • Web – directed network • Run in a specific direction: from one page to another • Dificulty: many pages are dynamically generated

15. Social Networks • Collection of social ties among friends • A network of people or group of people such as firms • Vertecies - People or groups • Edges – connections of some kind • Friendship or acquaintances , working relations, sexual • Business relations • Sociology • Increas in complexity due to • Travel, technological advences, global communication, digital interaction • Exampe: Actor network • Wayne Zachary’s karate club - small 34 members • Figure 1.2 of N-N • Facebook or MS Instant messaging – large data

16. Economic Netwoks • Special types of social networks • Vertecies- firms, countries, industries • Edges – trading relationships between companies or countries- • Global manifacturing operations – network of suppliers • Media companies – network of advertizers • Spread of local breakdown to • Cascading failures or financial crisis

17. Biological Networks • Logical abstract • Interractions between genes and/or proteins • Betweenmolecules in the cells metabolic pathways • Interractions physical but links not • Possibility of inerraction molecules • Food web: Ecological, predetor-pray networks • Vertecies – species • Directed Links – predation of one by onother • Physical: • Nervous system, neurons in the brain • Blood vessels

20. How do we reason about networks? • Empirical: Study network data to find organizational principles • How do we measure and quantify networks? • Mathematical models: Graph theory and statistical models • Models allow us to understand behaviors and distinguish surprising from expected phenomena • Algorithms for analyzing graphs • Hard computational challenges

21. Properties of Networks • Structure • Behavior • Dynamcs • On networks – processes on .. • Of networks • Coevolution • Visualization – small networks • Metrics • centrality: • Quantifies how important vertices are • Degreeof a node: number of edges attached to a node

22. Structure • A language for structural features of networks • Complxities • Parts that are more or less densely interconnected • Central cores • Participants can be more central or peripherial

23. Hubs: vertices with unusually high degree • Observed in many networks • Algorithms for • analyzing and uderstaning • network data • Measurements of network properties

24. Small world effect • Milgram experiment • 6 degrees of seperation • Internet • Computer are few hops away

25. Clusters or Communities in Networks • Social networks – break down into subcommunities • Knit friends or acquantions • Business relationships of companies • Clustered sets • Community detection techniwues

26. Behavior and Dynamics • Structure – starting point • Connectedness at the level of structure • Who is linked to whom • At the level of behavior • İndividual’s actions – consequenses • Outcomes of anyone

27. Information Networks • www: links among Web pages • How pages are related • How groups of communities • Which pages are more prominent or important • Search engines - Google • Network structure - evaluate • quality and relevance of web pages • Not number of links it receives • A page is prominent if receives link from prominent pages

28. Processes on Networks • Failure and resilience • Diffusion epidemics • Search

29. Dynamics on and of networks • coevolution of networks • structure – proceses on networks

30. Network Dynamics – Structural Effects • How people influence each other • Taking into acount structure of the network • The underlaying mechanizms • İnformation and • population level • Local level - network • İn the structure links friends • Aligning behavior with immediate friends rather then population as a whole

31. Search • The way people explore social contact for information • Effectiveness of performing these tasks – structure of networks

32. Network Models • Mathematical modelsof networks • Random graphs and extnsions • Small-world model • Network growth models

33. MIS 644 • MIS 644 Social Network Analysis • Web www.mis.boun.edu.tr/badur/MIS644 • Books • Network Crowds • M. Newman, Networks

34. Course Outlines • Introduction to networks • Course overview • Basic Concepts • Graph theory • Verious types of networks • Metrics • path, components, • Centrality metrics • degree, betweenness, closeness, • eigen value, • Clique, clusters • Paths, components, degree distribution, clustering, degree correlations (assortativity) • Metrics for weighted spatial networks • Properties of real networks

35. Properties of real networks • Shortest paths and small-world property • Scale-free property and heavy-tailed degree distributions • Clustering coeficients • Hierarchy - Modularity • Network motifs • Network models • Random networks (Poisson and with a given degree distribution) • Watts-Strogatz model • Preferential attachment and its variants • Optimization-based network formation models • Exponential random graphs

36. Community detection methods • Strength of weak ties • Graph partitioning - Focus on spectral partitioning algorithm • Modularity maximization methods • Spectral partitioning • Hierarchical clustering - divisive and agglomerative methods • Overlapping communities, dynamic communities, • Statistical properties of community structures • Statistical analysis of network data • Network sampling methods • Bias in network sampling • Network inference based on cross-correlations

37. Dynamics of networks • Percolation and network resilience • Random and non-random removel of vertices • Network epidemics • SI, SIS, SIR models • Network immunization • Identification of major spreaders • Social networks and influence • Information and behavior spreading - measurements and models • Influence maximization • Outbreak detection

38. Decentralized search on networks • Coevolutionary dynamics • Adaptive coevolutionary networks • Coevolutionary dynamics in opinion/consensus formation • Coevolutionary dynamics in epidemics • Network of networks - Interdependent networks • Instances of interdependent networks in practice • Layered networks • Cascade phenomena in intedependent networks

39. Structural balance • Structure of the Web • Link analysis and Web search • PageRank HITS (as centrality metrics) • Kronecker graphs

40. Prereguisits • Elementary knowledge of linear algebra, calculus • probability and statistics • basic knowledge of algorithms • no programming language

41. Work Load • Project • mid reports • final report • presentgation • Paper presentations • mostly applied papers • Final