Centrality and Power

1. Centrality and Power 周红豆 光华管理学院市场营销系

2. Power • Figure 10.1. "Star" network they have power because they can dominate others -- ego's power is alter'sdependence. Power is both a systemic (macro) and relational (micro) property.  Micro: i.e. it describes relations between actors; Macro:i.e. one that describes the entire population Having “a favored position” “more opportunities” “fewer constraints”

3. Power • Figure10.2.  "Line“ network • Figure 10.3.  "Circle" network they have power because they can dominate others -- ego's power is alter'sdependence. Power is both a systemic (macro) and relational (micro) property.  Micro: i.e. it describes relations between actors; Macro:i.e. one that describes the entire population Having “a favored position” “more opportunities” “fewer constraints”

5. Degree centrality • Figure 10.4.  Knoke's information exchange network Actors who have more ties to other actors may be advantaged positions. less dependent on other individuals; have access to; be able to call on more of the resources of the network as a whole; third-parties and deal makers in exchanges among others, and are able to benefit from this brokerage. Actors who have unusually high out-degree are actors who are able to exchange with many others, or make many others aware of their views. Actors who display high out-degree centrality are often said to be influential actors.

7. Degree centrality:  Freeman's approach • Network>Centrality>Degree • Figure 10.5.  Freeman degree centrality and graph centralization of Knoke information network 

9. Closeness power also comes from acting as a "reference point" by which other actors judge themselves, and by being a center of attention who's views are heard by larger numbers of actors.Actors who are able to reach other actors at shorter path lengths, or who are more reachable by other actors at shorter path lengths have favored positions.

10. Path distances • Network>Centrality>Closeness

11. Figure 10.10.  Geodesic path closeness centrality for Knoke information network

12. Betweenness centrality • Freeman's approach to binary relations • Network>Centrality>Betweenness>Nodes The third reason that actor A is advantaged in the star network is because actor A lies between each other pairs of actors, and no other actors lie between A and other actors.

13. Figure 10.17.  Freeman node betweenness for Knoke information network

14. Measurement • V Latora and M M archiori.A measure of centrality based on network efficiency.[J] New Journal of Physics9 (2007) 188

15. Degree centrality

16. Closeness centrality

17. Betweenness centrality

18. Extensions

19. Delta centralities: the information centrality

22. APPLICATION:SIMPLE EXAMPLE

24. APPLICATION: Individuals and groups

28. Centrality VS. • Power

30. Application :WORLD CITY Zachary Nea . [J]Differentiating Centrality and Power in the World City Network. Urban Studies.2011, 48(13) 2733–2748.

31. the number of direct connections

32. In addition to allowing finer-grained dis tinctions among cities’ network positions, the recursive measures also allow cities’ centrality and power to be considered separately. Using degree centrality, Paris appears to be moderately central (0.57), which may be interpreted as evidence of second-tier world city status. However, a more complete picture of Paris’ world city status emerges when centrality and power are treated as distinct concepts. Paris has a relatively low recursive centrality score (0.27), but has the highest recursive power score in the network (1.0). These results might suggest that, while Paris may not be a hub of capital accumulation, it is a centre of command-and-control, serving as an intermediary that connects other European cities (such as Milan, Vienna) to the world. That is, to view Paris as a second-tier world city obscures its more nuanced role as a minor site of flow concentration but a major site of flow influence. A similar but reversed story emerges in the case of Sydney which, like Paris, appears moderately central using degree centrality (0.43) but, unlike Paris, is revealed to be highly central (0.64) and minimally powerful (0.16) when the recursive measures are used.

33. The cases of Sydney and Paris mirror the cases of the focal cities in Figure 1’s network A and network B. Despite both cities having similar degree centrality, Sydney’s position in the Friedmann network closely resembles the ‘central but not powerful’ focal city in network A, while Paris’ position more closely resembles the ‘powerful but not central’ focal city in network B.