Chapter7 Connection and D istance

1. Chapter7 Connection and Distance YUAN Ying

2. Contents • Networks and actorsAn example: Knoke's information exchange • Connection • Basic demographics • Density • Reachability • Connectivity • Distance • Walks etc. • Geodesic distance, eccentricity, and diameter • Flow • Discussion & application in marketing

3. Knokeinformation exchange directed graph & adjacency matrix

4. Connection: basic demographics • Network size • Actor degree • Out-degree • In-degree • Distribution of actor degree

5. Out-degree statistics for Knoke information exchange Out-degree

6. In-degree statistics for Knoke information exchange

7. Different actors play different role in the network

8. Other aspects of connectedness • Density • the proportion of all possible ties that are actually present • Reachability • An actor is "reachable" by another if there exists any set of connections by which we can trace from the source to the target actor. • Connectivity • the number of nodes that would have to be removed in order for one actor to no longer be able to reach another

9. ReachabilityofKnoke Fully connected!

10. Point connectivity of Knoke

11. Distance: simple graph • Walks • A walk is a sequence of actors and relations that begins and ends with actors.

12. Distance: simple graph • Trail A trail between two actors is any walk that includes a given relation no more than once

13. Distance: simple graph • Path A path is a walk in which each other actor and each other relation in the graph may be used at most one time.

14. Distance: directed graph Walks/trail/path

15. Numbers of walks in Knoke information network

16. Numbers of walks in Knoke information network ?

17. Distance • Geodesic distance • The number of relations in the shortest possible walk from one actor to another • Often the “optimal” or most “efficient” connection between two actors • Often assume that actors will use the geodesic path when alternatives are available.

18. Other occasions regarding distance Measure of the strength of ties Measure of the cost of making a connection Measure of the probability that a link will be used

19. Distance to NearnessTransformation Multiplicative nearness Additive nearness Frequency decay Linear nearness Exponential decay

20. Distance to NearnessTransformation • Multiplicative nearness • Divides the distance by the largest possible distance between two actors (?)

21. Distance to NearnessTransformation • Additive nearness • Subtracts the actual distance between two actors from the number of nodes

22. Distance to NearnessTransformation • Frequency decay • 1 minus the proportion of other actors who are as close or closer to the target as ego is. • The idea is that if there are many other actors closer to the target you are trying to reach than yourself, you are effectively “more distant”

23. Distance to NearnessTransformation • Linear nearness • Rescales distance by reversing the scale (i.e. the closest becomes the most distant, the most distant becomes the nearest) and re-scoring to make the scale range from 0 (closest pair of nodes) to 1 (most distant pair of nodes)

24. Distance to NearnessTransformation • Exponential decay • turns distance into nearness by weighting the links in the pathway with decreasing values as they fall farther away from ego. • With an attenuation factor of .5, for example, a path from A to B to C would result in a distance of 1.5.

25. Geodesic distances for Knoke information exchange

26. Distance • Eccentricity (individual) • For each actor, that actor's largest geodesic distance is called the eccentricity -- a measure of how far a actor is from the furthest other. • Diameter (whole network) • The largest geodesic distance in the (connected) network.

27. # of geodesic paths for Knoke information exchange - an index of connection redundancy Vs.

28. Flow • How does a rumor become a truth? • How soon you hear it vs. • how many times you hear it from different people • Maximum flow • how many different actors in the neighborhood of a source lead to pathways to a target • Flow vs. walk/trail/path?

29. Maximum flow for Knoke information network Attention: #6, #8, #10

30. Knokeinformation exchange directed graph & adjacency matrix

31. Summary • Connection • Basic demographics • Network size • Actor degree • Out-degree • In-degree • Distribution of actor degree • Density • Reachability • Connectivity • Distance • Walks, trails, paths • Geodesic distance, eccentricity, and diameter • Flow

33. Discussion • Macro • Whole • Structure • Micro • Individual • Behavior What’s the difference between social network researches in sociology vs. marketing?

34. Application of social network analysis to marketing • . Word-of-mouth (WOM) vs. Traditional marketing • How to influence consumers’ behavior/opinion through social network? • WOM diffusion in online network vs. offline network

35. Harris interactive - a market research firm Since1975

36. Harris Interactive Reading #1Word-of-mouth research: principles and applications

38. Jo Brown, Amanda J. Broderick, And Nick Lee Reading #2Word of mouth communication within online communities: conceptualizing the online social network

39. Thank you!