1. Networked Life and Social Networks Thanks to Michael Kearns, James Moody, Anna Nagurney, Colexn

2. What we have covered What is IR Evaluation Tokenization and properties of text Web crawling Query models Vector methods Measures of similarity Indexing Inverted files Spam and SEO Google and Link Analysis Today - new directions in search –Social networks and networking - web 2.0 –Relationships to other network models - pagerank

3. Social networks vs social networking Social networks are links of actors and their relationships usually represented as a graph or network Social networking is the actual implementation of social networks in the digital world or media –A social network service focuses on building and reflecting of social networks or social relations among people, e.g., who share interests and/or activities. A social network service essentially consists of a representation of each user (often a profile), his/her social links, and a variety of additional services. Most social network services are web based and provide means for users to interact over the internet, such as e-mail and instant messaging.

4. Facebook vs Google

5. Web 2.0 A perceived second generation of web development and design, that aims to facilitate communication, secure information sharing, interoperability, and collaboration on the World Wide Web. Web 2.0 concepts have led to the development and evolution of web-based communities, hosted services, and applications such as social- networking sites, video-sharing sites, wikis, blogs, and folksonomies.

6. Social Media Information content created by people using highly accessible and scalable publishing technologies that is intended to facilitate communications, influence and interaction with peers and with public audiences, typically via the Internet and mobile communications networks. The term most often refers to activities that integrate technology, telecommunications and social interaction, and the construction of words, pictures, videos and audio. Businesses also refer to social media as user- generated content (UGC) or consumer-generated media (CGM).

7. Social Media on Web 2.0 Multimedia –Photo-sharing: Flickr –Video-sharing: YouTube –Audio-sharing: imeem Entertainment –Virtual Worlds: Second Life –Online Gaming: World of Warcraft News/Opinion –Social news: Digg, Reddit –Reviews: Yelp, epinions Communication –Microblogs: Twitter, Pownce –Events: Evite Social Networking Services: –Facebook, LinkedIn, MySpace

8. Top 10 Websites Googe Microsoft Yahoo! AOL Wikimedia eBay CBS Fox Interactive Media Amazon Sites Facebook Source: comScore as of August 2008

9. Social Network Service A social network service focuses on building online communities of people who share interests and/or activities, or who are interested in exploring the interests and activities of others.online communities Most social network services are web based and provide a variety of ways for users to interact, such as e-mail and instant messaging services.web based e-mailinstant messaging

10. Popular Social Networking Sites by Location North America –MySpace and Facebook, Nexopia (mostly in Canada)MySpaceFacebookNexopiaCanada South and Central America –Orkut, Facebook and Hi5OrkutFacebookHi5 Europe –Bebo,Facebook, Hi5, MySpace, Tagged, Xing and SkyrockBeboFacebookHi5MySpaceTaggedXing Skyrock Asia and Pacific –Friendster, Orkut, Xiaonei and CyworldFriendsterOrkutXiaoneiCyworld

11. Usage of Social Network

12. Types of Social Networking Services Profile-based Content-based White-label Multi-user Virtual environments Mobile Micro-blogging Social Search

13. Profile-based primarily organized around members’ profile pages – pages that mainly consist of information about an individual member, including the person’s picture and details of interests, likes and dislikes. Bebo, Facebook and MySpace are all good examples of profile-based services.BeboFacebookMySpace

14. Content-based In these services, the user’s profile remains an important way of organizing connections, but plays a secondary role to the posting of content. Examples of content-based communities: –YouTube.com for video sharing –Last.fm, in which the content is arranged by software that monitors and represents the music that users listen to. –Photo-sharing site like Flickr.com.

15. White-label Offer some group-building functionality, which allows users to form mini- communities within sites. Example sites: –PeopleAggregator –Ning –Colexn

16. Multi-user Virtual Environment allow users to interact with each other’s avatars users have profile cards, their functional profiles are the characters they customize or build and control. Friends lists are usually private and not publicly shared or displayed. Example Sites: –Second LifeSecond Life –World of WarcraftWorld of Warcraft

17. Mobile Social Networking Many social networking sites, for example MySpace and Twitter, offer mobile phone versions of their services, allowing members to interact with their friends via their phones.MySpace Twitter mobile-led and mobile-only communities include profiles and media-sharing just as with web-based social networking services. MYUBO, for example, allows users to share and view video over mobile networksMYUBO

18. Micro-blogging Allows you to publish short (140 characters, including spaces) messages publicly or within contact groups. These services are designed to work as mobile services, but are popularly used on the web as well. Example Services –TwitterTwitter –JaikuJaiku

19. Social Search Social search engines are an important web development which utilise the popularity of social networking services. There are various kinds of social search engine, but sites like Wink and Spokeo generate results by searching across the public profiles of multiple social networking sites, allowing the creation of web-based dossiers on individuals.WinkSpokeo This type of people search cuts across the traditional boundaries of social networking site membership, although any data retrieved should already be in the public domain.

20. Things you can do in a Social Network Communicating with existing networks, making and developing friendships/contacts Represent themselves online, create and develop an online presence Viewing content/finding information Creating and customizing profiles Authoring and uploading content Adding and sharing content Posting messages – public & private Collaborating with other people

21. What we’ve covered Physical, social, biological, etc –Hybrids Static vs dynamic Local vs global Measurable and reproducible

22. Networked Life Physical, social, biological, etc –Hybrids Static vs dynamic Local vs global Measurable and reproducible

23. North American Power Grid Points: power stations Operated by companies Connections embody business relationships Food for thought: –2003 Northeast blackout

24. The Human Brain Purely biological network Links are physical Interaction is electrical Food for thought: –Do neurons cooperate or compete?

25. The Premise of Networked Life It makes sense to study these diverse networks together. The Commonalities: –Formation (distributed, bottom-up, “organic”,…) –Structure (individuals, groups, overall connectivity, robustness…) –Decentralization (control, administration, protection,…) –Strategic Behavior (economic, free riding, Tragedies of the Common) An Emerging Science: –Examining apparent similarities between many human and technological systems & organizations –Importance of network effects in such systems How things are connected matters greatly Details of interaction matter greatly The metaphor of viral spread Dynamics of economic and strategic interaction –Qualitative and quantitative; can be very subtle –A revolution of measurement, theory, and breadth of vision

26. Who’s Doing All This? Computer & Information Scientists –Understand and design complex, distributed networks –View “competitive” decentralized systems as economies Social Scientists, Behavioral Psychologists, Economists –Understand human behavior in “simple” settings –Revised views of economic rationality in humans –Theories and measurement of social networks Physicists and Mathematicians –Interest and methods in complex systems –Theories of macroscopic behavior (phase transitions) All parties are interacting and collaborating

27. Examples Theories Apps in all areas

28. The Networked Nature of Society Networks as a collection of pairwise relations Examples of (un)familiar and important networks –social networks –content networks –technological networks –biological networks –economic networks The distinction between structure and dynamics A network-centric overview of modern society.

29. Gnutella Peers Points are still machines… but are associated with people Links are still physical… but may depend on preferences Interaction: content exchange Food for thought: “free riding”

30. Internet, Router Level A purely technological network? “Points” are physical machines “Links” are physical wires Interaction is electronic What more is there to say?

31. Foreign Exchange Points: sovereign nations Links: exchange volume A purely virtual network

32. Contagion, Tipping and Networks Epidemic as metaphor The three laws of Gladwell: –Law of the Few (connectors in a network) –Stickiness (power of the message) –Power of Context The importance of psychology Perceptions of others Interdependence and tipping Paul Revere, Sesame Street, Broken Windows, the Appeal of Smoking, and Suicide Epidemics

33. Graph & Network Theory Networks of vertices and edges Graph properties: –cliques, independent sets, connected components, cuts, spanning trees,… –social interpretations and significance Special graphs: –bipartite, planar, weighted, directed, regular,… Computational issues at a high level

34. Social Networks A social network is a social structure of people, related (directly or indirectly) to each other through a common relation or interest Social network analysis (SNA) is the study of social networks to understand their structure and behavior (Source: Freeman, 2000)

35. Social Network Theory Metrics of social importance in a network: –degree, closeness, between-ness, clustering… Local and long-distance connections SNT “universals” –small diameter –clustering –heavy-tailed distributions Models of network formation –random graph models –preferential attachment –affiliation networks Examples from society, technology and fantasy

36. The Web as a Network Empirical web structure and components Web and blog communities Web search: –hubs and authorities –the PageRank algorithm The Main Streets and “dark alleys” of the web The algorithmic and social implications of network structure.

37. Towards Rationality: Emergence of Global from Local Beyond the dynamics of transmission Context, motivation and influence The madness/wisdom of crowds: –thresholds and cascades –mathematical models of tipping –the market for lemons –private preferences and global segregation

38. Interdependent Security and Networks Security investment and Tragedies of the Commons Catastrophic events: you can only die once Fire detectors, airline security, Arthur Anderson,… Blending network, behavior and dynamics.

39. Network Economics Buying and selling on a network Modeling constraints on trading partners Local imbalances of supply and demand Preferential attachment, price variation, and the distribution of wealth The effects of network structure on economic outcomes.

40. Modern Financial Markets Stock market networks –correlation of returns Market microstructure –limit and market orders –order books and electronic crossing networks –network, connectivity and data issues Quantitative trading –VWAP trading, market making –limit order power laws Herd behavior in trading Economic theory and financial markets Behavioral economics and finance Impacts of the Internet on financial markets A study of the network that runs the world.

41. Definition of Social Networks “ A social network is a set of actors that may have relationships with one another. Networks can have few or many actors (nodes), and one or more kinds of relations (edges) between pairs of actors. ” (Hannemann, 2001)

42. History (based on Freeman, 2000) 17th century: Spinoza developed first model 1937: J.L. Moreno introduced sociometry; he also invented the sociogram 1948: A. Bavelas founded the group networks laboratory at MIT; he also specified centrality

43. Social Networking –Large number of sites available throughout the worldLarge number

44. History (based on Freeman, 2000) 1949: A. Rapaport developed a probability based model of information flow 50s and 60s: Distinct research by individual researchers 70s: Field of social network analysis emerged. –New features in graph theory – more general structural models –Better computer power – analysis of complex relational data sets

45. “Structural Analysis: from method and metaphor to theory and substance.” H. White: “The presently existing, largely categorical descriptions of social structure have no solid theoretical grounding; furthermore, network concepts may provide the only way to construct a theory of social structure.” (p.25) Form Vs. Content Integration of large-scale social systems Foundations Theory

46. Social network analysis is: a set of relational methods for systematically understanding and identifying connections among actors. SNA is motivated by a structural intuition based on ties linking social actors is grounded in systematic empirical data draws heavily on graphic imagery relies on the use of mathematical and/or computational models. Social Network Analysis embodies a range of theories relating types of observable social spaces and their relation to individual and group behavior. Introduction

47. What are social relations? A social relation is anything that links two actors. Examples include: KinshipCo-membership FriendshipTalking with LoveHate ExchangeTrust CoauthorshipFighting Introduction

48. What properties relations are studied? The substantive topics cross all areas of sociology. But we can identify types of questions that social network researchers ask: 1) Social network analysts often study relations as systems. That is, what is of interest is how the pattern of relations among actors affects individual behavior or system properties. Introduction

49. High Schools as Networks Introduction

52. Why do Networks Matter?Local vision Introduction

53. Why do Networks Matter?Local vision Introduction

54. Representation of Social Networks Matrices Graphs Nick Ann Rob Sue

55. Graphs - Sociograms (based on Hanneman, 2001) Labeled circles represent actors Line segments represent ties Graph may represent one or more types of relations Each tie can be directed or show co- occurrence –Arrows represent directed ties

56. Graphs – Sociograms (based on Hanneman, 2001) Strength of ties: –Nominal –Signed –Ordinal –Valued

57. Visualization Software: KrackplotKrackplot

58. Connections Size –Number of nodes Density –Number of ties that are present vs the amount of ties that could be present Out-degree –Sum of connections from an actor to others In-degree –Sum of connections to an actor Diameter –Maximum greatest least distance between any actor and another

59. Some Measures of Distance Walk (path) –A sequence of actors and relations that begins and ends with actors Geodesic distance (shortest path) –The number of actors in the shortest possible walk from one actor to another Maximum flow –The amount of different actors in the neighborhood of a source that lead to pathways to a target

60. Some Measures of Power (based on Hanneman, 2001) Degree –Sum of connections from or to an actor Closeness centrality –Distance of one actor to all others in the network Betweenness centrality –Number that represents how frequently an actor is between other actors’ geodesic paths

61. Cliques and Social Roles (based on Hanneman, 2001) Cliques –Sub-set of actors More closely tied to each other than to actors who are not part of the sub-set Social roles –Defined by regularities in the patterns of relations among actors

62. SNA applications Many new unexpected applications plus many of the old ones Marketing Advertising Economic models and trends Political issues –Organization Services to social network actors –Travel; guides –Jobs –Advice Human capital analysis and predictions Medical Epidemiology Defense (terrorist networks)

63. Examples of Applications (based on Freeman, 2000) Visualizing networks Studying differences of cultures and how they can be changed Intra- and interorganizational studies Spread of illness, especially HIV

64. The unit of interest in a network are the combined sets of actors and their relations. We represent actors with points and relations with lines. Actors are referred to variously as: Nodes, vertices, actors or points Relations are referred to variously as: Edges, Arcs, Lines, Ties Example: a b ce d Foundations Data

65. Social Network data consists of two linked classes of data: a)Nodes: Information on the individuals (actors, nodes, points, vertices) Network nodes are most often people, but can be any other unit capable of being linked to another (schools, countries, organizations, personalities, etc.) The information about nodes is what we usually collect in standard social science research: demographics, attitudes, behaviors, etc. Often includes dynamic information about when the node is active b) Edges: Information on the relations among individuals (lines, edges, arcs) Records a connection between the nodes in the network Can be valued, directed (arcs), binary or undirected (edges) One-mode (direct ties between actors) or two-mode (actors share membership in an organization) Includes the times when the relation is active Graph theory notation: G(V,E) Foundations Data

66. In general, a relation can be: (1) Binary or Valued (2) Directed or Undirected a b ce d Undirected, binary Directed, binary a b ce d a b ce d Undirected, Valued Directed, Valued a b ce d 13 4 2 1 The social process of interest will often determine what form your data take. Almost all of the techniques and measures we describe can be generalized across data format. Foundations Data

67. Ego-Net Global-Net Best Friend Dyad Primary Group 2-step Partial network Foundations Data and social science

68. We can examine networks across multiple levels: 1) Ego-network - Have data on a respondent (ego) and the people they are connected to (alters). Example: terrorist networks - May include estimates of connections among alters 2) Partial network - Ego networks plus some amount of tracing to reach contacts of contacts - Something less than full account of connections among all pairs of actors in the relevant population - Example: CDC Contact tracing data Foundations Data

69. 3) Complete or “Global” data - Data on all actors within a particular (relevant) boundary - Never exactly complete (due to missing data), but boundaries are set -Example: Coauthorship data among all writers in the social sciences, friendships among all students in a classroom We can examine networks across multiple levels: Foundations Data

70. Working with pictures. No standard way to draw a sociogram: which are equal? Foundations Graphs

71. Network visualization helps build intuition, but you have to keep the drawing algorithm in mind: Tree-Based layouts Most effective for very sparse, regular graphs. Very useful when relations are strongly directed, such as organization charts, internet connections, Spring-embeder layouts Most effective with graphs that have a strong community structure (clustering, etc). Provides a very clear correspondence between social distance and plotted distance Two images of the same network Foundations Graphs

72. Network visualization helps build intuition, but you have to keep the drawing algorithm in mind: Tree-Based layouts Spring-embeder layouts Two images of the same network Foundations Graphs

73. Network visualization helps build intuition, but you have to keep the drawing algorithm in mind. Hierarchy & Tree models Use optimization routines to add meaning to the “Y-axis” of the plot. This makes it possible to easily see who is most central because of who is on the top of the figure. Usually includes some routine for minimizing line- crossing. Spring Embedder layouts Work on an analogy to a physical system: ties connecting a pair have ‘springs’ that pull them together. Unconnected nodes have springs that push them apart. The resulting image reflects the balance of these two features. This usually creates a correspondence between physical closeness and network distance. Foundations Graphs

74. Foundations Graphs

75. Using colors to code attributes makes it simpler to compare attributes to relations. Here we can assess the effectiveness of two different clustering routines on a school friendship network. Foundations Graphs

76. As networks increase in size, the effectiveness of a point-and-line display diminishes - run out of plotting dimensions. Insights from the ‘overlap’ that results in from a space-based layout as information. Here you see the clustering evident in movie co-staring for about 8000 actors. Foundations Graphs

77. This figure contains over 29,000 social science authors. The two dense regions reflect different topics. Foundations Graphs

78. As networks increase in size, the effectiveness of a point-and-line display diminishes, because you simply run out of plotting dimensions. I’ve found that you can still get some insight by using the ‘overlap’ that results in from a space-based layout as information. This figure contains over 29,000 social science authors. The two dense regions reflect different topics. Foundations Graphs

79. Adding time to social networks is also complicated, run out of space to put time in most network figures. One solution: animate the network - make a movie! Here we see streaming interaction in a classroom, where the teacher (yellow square) has trouble maintaining order. The SoNIA software program (McFarland and Bender- deMoll)SoNIA Foundations Graphs and time

80. Graphs are cumbersome to work with analytically, though there is a great deal of good work to be done on using visualization to build network intuition. Recommendation: use layouts that optimize on the feature you are most interested in. Foundations Methods

81. A graph is vertices and edges A graph is vertices joined by edges –i.e. A set of vertices V and a set of edges E A vertex is defined by its name or label An edge is defined by the two vertices which it connects, plus optionally: –An order of the vertices (direction) –A weight (usually a number) Two vertices are adjacent if they are connected by an edge A vertex’s degree is the no. of its edges E L B M P 200 60 130 190 450 210

82. Directed graph (digraph) E L B M P 200 60 130 190 450 210 Each edge is an ordered pair of vertices, to indicate direction –Lines become arrows The indegree of a vertex is the number of incoming edges The outdegree of a vertex is the number of outgoing edges

83. Traversing a graph (1) A path between two vertices exists if you can traverse along edges from one vertex to another A path is an ordered list of vertices length: the number of edges in the path cost: the sum of the weights on each edge in the path cycle: a path that starts and finishes at the same vertex –An acyclic graph contains no cycles E L B M P 200 60 130 190 450 210

84. Traversing a graph (2) Undirected graphs are connected if there is a path between any pair of vertices Digraphs are usually either densely or sparsely connected –Densely: the ratio of number of edges to number of vertices is large –Sparsely: the above ratio is small E L B M P

85. Two graph representations: adjacency matrix and adjacency list Adjacency matrix –n vertices need a n x n matrix (where n = |V|, i.e. the number of vertices in the graph) - can store as an array –Each position in the matrix is 1 if the two vertices are connected, or 0 if they are not –For weighted graphs, the position in the matrix is the weight Adjacency list –For each vertex, store a linked list of adjacent vertices –For weighted graphs, include the weight in the elements of the list

86. Representing an unweighted, undirected graph (example) 0 1 2 3 4 0123401234 0 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 Adjacency matrix 13 023 134 012 2 0123401234 Adjacency list 0:E 3:L 2:B 1:M 4:P

87. Representing a weighted, undirected graph (example) 0:E 3:L 2:B 1:M 4:P 200 60 130 190 450 210 0 1 2 3 4 0123401234 0 210 0 450 0 210 0 60 190 0 0 60 0 130 200 450 190 130 0 0 0 0 200 0 0 Adjacency matrix 3;450 2;603;190 3;1304;200 1;1902;130 1;210 0;210 1;60 0;450 2;200 0123401234 Adjacency list

88. Representing an unweighted, directed graph (example) 0 1 2 3 4 0123401234 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 Adjacency matrix 1 3 13 0 2 0123401234 Adjacency list 0:E 3:L 2:B 1:M 4:P

89. Comparing the two representations Space complexity –Adjacency matrix is O(|V| 2 ) –Adjacency list is O(|V| + |E|) |E| is the number of edges in the graph Static versus dynamic representation –An adjacency matrix is a static representation: the graph is built ‘in one go’, and is difficult to alter once built –An adjacency list is a dynamic representation: the graph is built incrementally, thus is more easily altered during run-time

90. Algorithms involving graphs Graph traversal Shortest path algorithms –In an unweighted graph: shortest length between two vertices –In a weighted graph: smallest cost between two vertices Minimum Spanning Trees –Using a tree to connect all the vertices at lowest total cost

91. Graph traversal algorithms When traversing a graph, we must be careful to avoid going round in circles! We do this by marking the vertices which have already been visited Breadth-first search uses a queue to keep track of which adjacent vertices might still be unprocessed Depth-first search keeps trying to move forward in the graph, until reaching a vertex with no outgoing edges to unmarked vertices

92. Shortest path (unweighted) The problem: Find the shortest path from a vertex v to every other vertex in a graph The unweighted path measures the number of edges, ignoring the edge’s weights (if any)

93. Shortest unweighted path: simple algorithm 1Mark all vertices with d v = infinity 2Select a starting vertex s, and set d s = 0, and set shortest = 0 3For all vertices v with d v = shortest, scan their adjacency lists for vertices w where d w is infinity –For each such vertex w, set d w to shortest+1 4Increment shortest and repeat step 3, until there are no vertices w For a vertex v, d v is the distance between a starting vertex and v

94. From pictures to matrices a b ce d Undirected, binaryDirected, binary a b ce d abcde a b c d e 1 1 1 1 1 1 1 abcde a b c d e 1 1 1 1 1 1 1 1 1 1 Foundations Build a socio-matrix

95. From matrices to lists abcde a b c d e 1 1 1 1 1 1 1 1 1 1 a b b a c c b d e d c e e c d a b b a b c c b c d c e d c d e e c e d Adjacency List Arc List Foundations Methods

96. Basic Measures For greater detail, see: http://www.analytictech.com/networks/graphtheory.htm Volume The first measure of interest is the simple volume of relations in the system, known as density, which is the average relational value over all dyads. Under most circumstances, it is calculated as: Foundations Basic Measures )1(    NN X 

97. Volume At the individual level, volume is the number of relations, sent or received, equal to the row and column sums of the adjacency matrix. abcde a b c d e 1 1 1 1 1 1 1 Node In-Degree Out-Degree a 11 b 2 1 c 13 d 2 0 e 12 Mean: 7/5 7/5 Foundations Basic Measures

98. d e c Reachability Indirect connections are what make networks systems. One actor can reach another if there is a path in the graph connecting them. a b ce d f bf a Foundations Data

99. Foundations Basic Matrix Operations One of the key advantages to storing networks as matrices is that we can use all of the tools from linear algebra on the socio-matrix. Some of the basics matrix manipulations that we use are as follows: 1)Definition A matrix is any rectangular array of numbers. We refer to the matrix dimension as the number of rows and columns abcde a b c d e 1 1 111 11 0 0 0 0 0 0 0 000 00 0 000 00 (5 x 5) W B 1 0 0 1 1 0 (5x2) Age 13 10 7 8 16 11 (5x1)

100. Foundations Basic Matrix Operations Matrix operations work on the elements of the matrix in particular ways. To do so, the matrices must be conformable. That means the sizes allow the operation. For addition (+), subtraction (-), or elementwise multiplication (#), both matrices must have the same number of rows and columns. For these operations, the matrix value is the operation applied to the corresponding cell values. 1 3 4 7 2 5 2 3 7 1 0 4 A=A=B=B= A+B = 3 6 11 8 2 9 A-B = -1 0 -3 6 2 1 A#B = 2 9 28 7 0 20 Multiplication by a scalar: 3A = 3 9 12 21 6 15

101. Matrix properties Addition contributes to the actors relations Multiplication sums over a trait. Negative values can occur –(friend, don’t care, enemy) = (1,0,-1) –Interpret operations carefully

102. Foundations Basic Matrix Operations The transpose (` or T ) of a matrix reverses the row and column dimensions. A t ij =A ji So a M x N matrix becomes an N x M matrix. a b c d e f T = a c e b d f

103. Foundations Basic Matrix Operations The matrix multiplication ( x ) of two matrices involves all elements of the matrix, and will often result in a matrix of new dimensions. In general, to be conformable, the inner dimension of both matrices must match. So: A 3x2 x B 2x3 = C 3 x 3 But A 3x3 x B 2x3 is not defined (actually a tensor) Substantively, adding ‘names’ to the dimensions will help us keep track of what the resulting multiplications mean: So multiplying (send x receive)x (send x receive) = (send x receive), giving us the two-step distances (the sender’s recipient's receivers).

104. Foundations Basic Matrix Operations The multiplication of two matrices A m x n and B n x q results in C m x q a b c d e f g h = ae+bg af+bh ce+dg cf+dh a b c d e f g h i j k l = ag+bj ah+bk ai+bl cg+dj ch+dk ci+dl eg+fg eh+fk ei+fl (3x2) (2x3) (3x3)

105. Foundations Basic Matrix Operations The powers (square, cube, etc) of a matrix are just the matrix times itself that many times. A 2 = AA or A 3 = AAA We often use matrix multiplication to find types of people one is tied to, since the ‘1’ in the adjacency matrix effectively captures just the people each row is connected to.

106. Basic Measures Reachability The distance from one actor to another is the shortest path between them, known as the geodesic distance. If there is at least one path connecting every pair of actors in the graph, the graph is connected and is called a component. Two paths are independent if they only have the two end- nodes in common. If a graph has two independent paths between every pair, it is biconnected, and called a bicomponent. Similarly for three paths, four, etc. Foundations Data

107. Calculate reachability through matrix multiplication. (see p.162 of W&F) a b c e d f X 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 X 2 2 0 2 0 0 0 0 2 0 1 1 2 2 0 4 1 1 0 0 1 1 2 1 1 0 1 1 1 2 1 0 2 0 1 1 2 X 3 0 4 0 2 2 4 4 0 6 1 1 0 0 6 2 5 5 6 2 1 5 2 3 1 2 1 5 3 2 1 4 0 6 1 1 0 Distance. 1 2 0 0 1 1. 1 2 2 2 2 1. 1 1 1 0 2 1. 1 2 0 2 1 1. 2 1 2 1 2 2. Distance. 1 2 3 3 1 1. 1 2 2 2 2 1. 1 1 1 3 2 1. 1 2 3 2 1 1. 2 1 2 1 2 2. Foundations Data Total # of directed walks for power n Minimal distance from one node to another

108. Mixing patterns Matrices make it easy to look at mixing patterns: connections among types of nodes. Simply multiply an indicator of category by the adjacency matrix. a b c e d f X 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 Race 1 0 0 1 1 0 X(Race) 2 0 1 1 2 2 0 2 1 1 Race`(X)Race= 4 2 2 6 B G BGBG Foundations Data B 4 to selves B 2 to G G 2 to B G 6 to selves

109. Matrix manipulations allow you to look at direction of ties, and distinguish symmetric from asymmetric ties. To transform an asymmetric graph to a symmetric graph, add it to its transpose. X 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 X T 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 2 0 0 0 2 0 1 0 0 0 1 0 1 2 0 0 1 0 1 0 0 2 1 0 Max Sym MIN Sym 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 Foundations Data Interpretation?

110. Graphs / matrices Analysis of social structure Visualization tools Other methods –Statistics Power laws –Bayesian graphs

111. Pr(page has k inlinks)  k -  [  2.1] Popular few receive disproportionate share of links  traffic,  prob SE indexing,  SE ranking Global web: Winners take all

112. Category-specific web: Winner’s don’t (quite) take all All US company homepages hist w/ exp  buckets (const on log scale) Strong deviation from pure power law Unimodal (  l.n.) body, power law tail Less skewed; many fare well against mode Pennock, Giles, et.al PNAS 2002

113. Applications of Networked Life Social structure in organizations Economic and business behavior Epidemiology Information discovery Design and robustness of networks …

114. SNA disciplines More diverse than expected! Sociology Political Science Business Economics Sciences Computer science Information science Others?

115. Citation Graph - social network Paper cites is cited by Note that journal citations nearly always refer to earlier work. Bibliographic coupling cocitation

116. Graphical Analysis of Hyperlinks on the Web - social network? This page links to many other pages (hub) Many pages link to this page (authority) 1 2 3 4 5 6

117. PageRank as social network analysis PageRank (social rank) “flowing” from pages to the pages they cite..1.09.05.03.08.03

118. SN on the web - services A social network service uses software to build online social networks for communities of people who share interests and activities or who are interested in exploring the interests and activities of others. - wikipedia Friending –Facebook –MySpace –LinkedIn –Second life This will only increase! Large complex, heterogeneous networks –Latour’s actor-network model Different entities connect actors –Coauthorship network connected by papers

119. example: networks of people and articles (e.g., citation and co-authorship networks) this image is from the system ReferalWeb by Henry Katz et al. at ATT Research http://foraker.research.att.com/refweb/version2/RefWeb.html

120. SNA and the Web 2.0 Wikis Blogs Folksonomies Collaboratories What next?

121. Computational SNA Models New models are emerging Very large network analysis is possible! Deterministic - algebraic –Early models still useful Statistical –Descriptive using many features Diameter, betweeness, Probabilistic graphs –Generative Creates SNA based on agency, documents, geography, etc. Community discovery and prediction

122. Graphical models Modeling the document generation Existing three generative models. Three variables in the generation of documents are considered: (1) authors; (2) words; and (3) topics (latent variable)

123. Theories used in SNA Graph/network –Heterogeneous graphs –Hypergraphs –Probabilistic graphs Economics/game theory Optimization Visualization/HCI Actor/Network Many more

124. Future of social networks? Tribes - Seth Godin Human flesh search engine –Internet mobbingInternet mobbing Will there be war?

125. Future of social networks? Top End User Predictions for 2010 - Gartner By 2012, Facebook will become the hub for social networks integration and Web socialization. Internet marketing will be regulated by 2015, controlling more than $250 billion in Internet marketing spending worldwide. By 2014, more than three billion of the world’s adult population will be able to transact electronically via mobile and Internet technology. By 2015, context will be as influential to mobile consumer services and relationships as search engines are to the Web. By 2013, mobile phones will overtake PCs as the most common Web access device worldwide.

126. Open questions Scalability Data acquisition and data rights Search (socialnetworkrank?) Trust Heterogeneous network analysis Business models!

127. What next? More personal search Mobile search Specialty search Freshness search ? “Search as a problem is only 5% solved” Udi Manber, 1st Yahoo, 2nd Amazon, now Google