签订房屋租赁合同的十大注意事项.pptx

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Lecture 5:
Network centrality
扁平工作汇报通用模版
Measures and Metrics
Knowing the structure of a network, we can calculate various useful quantities or measures that capture particular features of the network topology.
basis of most of such measures are from social network analysis
So far,
Degree distribution, Average path length, Density
Centrality
Degree, Eigenvector, Katz, PageRank, Hubs, Closeness, Betweenness, ….
Several other graph metrics
Clustering coefficient, Assortativity, Modularity, …
Characterizing networks:Who is most central?
network centrality
4
Which nodes are most ‘central’?
Definition of ‘central’ varies by context/purpose
Local measure:
degree
Relative to rest of network:
closeness, betweenness, eigenvector (Bonacich power centrality), Katz, PageRank, …
How evenly is centrality distributed among nodes?
Centralization, hubs and autthorities, …
centrality: who’s important based on their network position
indegree
In each of the following networks, X has higher centrality than Y according to
a particular measure
outdegree
betweenness
closeness
Outline
6
Degree centrality
1
Centralization
2
Betweenness centrality
3
Closeness centrality
4
Eigenvector centrality
5
Bonacich power centrality
6
Katz centrality
7
PageRank
8
Hubs and Authorities
9
He who has many friends is most important.
degree centrality (undirected)
When is the number of connections the best centrality measure?
people who will do favors for you
people you can talk to (influence set, information access, …)
influence of an article in terms of citations (using in-degree)
degree: normalized degree centrality
divide by the max. possible, . (N-1)
Prestige in directed social networks
when ‘prestige’ may be the right word
admiration
influence
gift-giving
trust
directionality especially important in instances where ties may not be reciprocated (. dining partners choice network)
when ‘prestige’ may not be the right word
gives advice to (can reverse direction)
gives orders to (- 〞 -)
lends money to (- 〞 -)
dislikes
distrusts
Extensions of undirected degree centrality - prestige
degree centrality
indegree centrality
a paper that is cited by many others has high prestige
a person nominated by many others for a reward has high prestige