Basic Network Concepts

Transcription

1 Basic Network Concepts

2 Basic Vocabulary Alice Graph Network Edges Links Nodes Vertices Chuck Bob

3 Edges Alice Chuck Bob

4 Edge Weights Alice Chuck Bob

5 Apollo 13 Movie Network Main Actors in Apollo 13 the Movie: Tom Hanks Kevin Bacon Gary Sinise Bill Paxton Ed Harris Actors are nodes. Edges connect actors who were in a movie together. Since all were in Apollo 13, this is not interesting. Let s make a new network that connects them if they were in an additional movie together.

6 Apollo 13 Movie Network Bill Paxton Magnificent Desolation: Walking on the Moon Magnificent Desolation: Walking on the Moon Tom Hanks The Green Mile Beyond All Boundaries Kevin Bacon Gary Sinise The Human Stain Ed Harris

7 Directed or Undirected? Tom Hanks Bill Paxton Kevin Bacon Gary Sinise Ed Harris

8 Adjacency List Tom Hanks TH,BP Bill Paxton TH,GS Kevin Bacon BP,GS GS,KB Gary Sinise Ed Harris GS,EH

9 Adjacency Matrix Bill Paxton Tom Hanks Kevin Bacon TH BP GS EH KB TH 1 2 BP 1 1 GS EH 1 KB 1 Gary Sinise Ed Harris

10 Shortest Path Length and Cliques A C D E F G H B

11 Cliques Tom Hanks Bill Paxton Kevin Bacon Gary Sinise Ed Harris

12 Connectedness Two nodes are connected if there is a path between them. A graph is connected if there is a path between every pair of nodes. In a directed graph, it is strongly connected if there is a directed path between each pair. It is weakly connected if there is a path between every pair if direction is ignored.

13 Hubs and Bridges J I K G H L M N R F P O Q D A E C B

14 Clusters A cluster is a group of nodes that are tightly connected tightly varies, but usually means they are more tightly connected than the network as a whole Does not need to be a clique Group in the lower left of previous graph is a cluster

15 Subnetworks Q A P O D E C B

16 Egocentric Networks Q A D E C B

17 Egocentric Networks Q A D E C B

18 Network Structure

19 Degree Distribution Tom Hanks Degrees Bill Paxton Gary Sinise Ed Harris Kevin Bacon Degree Distribution Tom Hanks Bill Paxton Gary Sinise Kevin Bacon Ed Harris Degree

20 Degree Distribution Degree Distribution Degree

21 Density Edges: 5 Total Possible Edges: 10 Density: 5/10 = 0.5 Tom Hanks Bill Paxton Kevin Bacon Gary Sinise Ed Harris

22 Density Nodes: 8 Edges: 12 Total Possible Edges:?? # Nodes * (# Nodes -1) 2 (8*7)/2 = 56/2 = 28 Density: 12/28 = 0.43

23 Clustering Coefficient Density of a node s 1.5 degree egocentric network (with the node itself excluded) is called its clustering coefficient. An important measure we will see later on.

24 Which Node is Most Important? B A K J I H C Q L R G D P M O N F E

25 Which Node is Most Important? J I K G H L M N R F P O Q D A E C B

26 Closeness Centrality J G I H P 1 O 1 Q 2 R F P O C Q D C 2 D 3 R 1 G 2 J 2 I 2 H 2 =18/10=1.8

27 Closeness Centrality J G I H P 2 O 2 Q 3 R F P O C Q D C 3 D 4 F 1 G 1 J 1 I 1 H 1 =19/10 =1.9

28 Closeness Centrality J I F 1 O 1 G R H Q 1 C 2 D 2 Q R 2 F P O C D G 3 J 3 I 3 H 3 =21/10 =2.1

29 Closeness Centrality J I F 1 O 1 G R H Q 1 C 2 D 2 Q R 2 F P O C D G 3 J 3 I 3 H 3 =21/10 =2.1

30 Degree Centrality K J G I H R=9 F=3 L N M R F P O Q D A E D=5 B=4 C B

31 Betweenness Centrality Measure of a node s influence Percentage of shortest paths that include a given node

32 Betweenness Centrality A B C E D F H G

33 Eigenvector Centrality Measure of a node s importance Iterative matrix computation that gives more weight to nodes if they are connected to influential nodes. The backbone to techniques like Google s PageRank which ranks web pages.

34 Connectivity and Cohesion Minimum number of nodes to remove before the network becomes disconnected. A B C D H E G F G F E D C A B Cohesion=1 Cohesion=2

35 Network

36 Exercise Open an assigned network in a network analysis tool like Gephi or NodeXL. Run statistics to compute centrality. Compare different centrality measures.

37 Visual Analysis of Networks

38 What is interesting about this network?

39 What makes a good visualization? Every node is visible For every node you can count its degree For every link you can follow it from source to destination Clusters and outliers are identifiable (Dunne and Shneiderman, 2009) We can t always do all of this, but it s a start

40 Is this a good visualization?

41 What about this one?

42 And this one?

43 And finally, this one?

44 Node Size and Color

45 Node Size and Color

46 Edge Weight

47 Visualization Issues Scale Too many nodes (~10,000 or more) or edges are almost impossible to visualize Dense networks may not reveal patterns

48 Example: Senate Voting Records

49 Filtering

50 Visualization Tools Gephi All platforms Stand alone program NodeXL Windows only Plugin for Microsoft Excel

51 In Class Exercise Load an assigned dataset into NodeXL or Gephi Create a visualization, using color, size, layout, and other features to tell a story or provide an insight into the data. Post your final visualization in a shared space

52 Tie Strength

53 Strong vs. Weak Ties Strong ties Trusted Close friends and family Weak ties Often part of other social circles Acquaintances, co-workers We talk about strong or weak ties, but in reality, there is a continuous spectrum

54 Mark Granovetter Foundational work in 1973, The Strength of Weak Ties Strong ties had been considered most important His work showed weak ties mattered

55 Getting a Job Carl Y. was doing commission sales for an encyclopedia firm, but was not doing well. He decided he would have to find a different job; meanwhile, he started driving a cab to bring in extra money. One passenger asked to be taken to the train station where he had to meet a friend. This friend turned out to be an old friend of Carl Y.'s, and asked him "what're you doing driving a cab?" When Mr. Y. explained, the friend offered him the job he now holds labor relations manager for a small company, owned by his friend. (Granovetter, 1974, p34) Granovetter, M Getting a Job: A Study of Contacts an

56 Getting a Job George C. was working as a technician for an electrical firm, with a salary of about $8000, and little apparent chance for advancement. While courting his future wife, he met her downstairs neighbor, the manager of a candy shop, a concession leased from a national chain. After they were married, Mr. C. continued to see him when visiting his mother-in-law. The neighbor finally talked him into entering a trainee program for the chain, and arranged an interview for him. Within three years, Mr. C. was earning nearly $30,000 in this business. (Granovetter, 1974, p. 49). Granovetter, M Getting a Job: A Study of Contacts an

57 Getting a Job Edward A., during high school, went to a party given by a girl he knew. There, he met her older sister's boyfriend, who was ten years older than himself. Three years later, when he had just gotten out of the service, he ran into him in a local hangout. In conversation, the boyfriend mentioned to Mr. A. that his company had an opening for a draftsman. Mr. A. applied for this job and was hired. (Granovetter, 1974, p. 76) Granovetter, M Getting a Job: A Study of Contacts an

58 Replicating Milgram s Six Degrees Send booklets from original participants to a target, unknown person (Lin, et al) show that successful chains made heavy use of weak ties

59 Weak Ties in Use Racial integration in schools Job satisfaction in psych hospital

60 The benefits of weak ties Connect people to different social circles, exposing them to more information Many more of them in a person s life than strong ties

61 The network of strong ties

62 Measuring Tie Strength Time Emotional Intensity Intimacy Reciprocal Services

63 Measuring Tie Strength Additional Features Social Distance Structural Emotional Support

64 Quantifying Measurements Time Emotional Intensity Intimacy Reciprocal Services Social Distance Structural Emotional Support

65 Measurement Overlaps

66 Network Structure Forbidden Triad

67 Network Structure - Bridges

68 Tie Strength and Propagation Strong ties more trusted Weak ties wider spread