HCC class lecture 22 comments

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HCC classlecture 22 comments
John Canny4/13/05
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Administrivia

• I wont be here Monday, but class as usual.

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Centrality, Prestige, Power

• Ways of articulating the importance of an actor
  in the network.
• Centrality is intuitively what the name implies.
  It matches the notion we have from communities
  of practice.

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Centrality

• Three notions
• Degree How many neighbors
• Closeness How far to furthest actor
• Betweeness How many pairs of actors can be
  joined by a path through this actor

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Centrality advanced measures

• Degree centrality can be applied iteratively
  (Bonacich). i.e. your centrality is proportional
  to the product of your neighbors and their
  centralities. Aka Bonacich or eigenvalue
  Centrality
• The actor weights come from the eigenvector of
  the largest eigenvalue of the adjacency matrix of
  the graph, or equivalently, the probability
  densities from a long random walk on the graph.

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Centrality Bonacich

• Bonacich centrality is generally acknowledged to
  be better than degree centrality for social
  networks.
• If you apply it to the web graph, you get
  Pagerank (Googles page quality algorithm).
• If you apply it to sentences in a text, you get
  TextRank (a good summarization algorithm).
• Caveat Many studies of web page quality have
  shown Pagerank to be equivalent to indegree.

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Power Bonacich

• Bonacich defined a notion of power which is
  different from centrality. It is based on the
  fact that if you are a neighbor of an actor with
  few neighbors, you have more power over them.
  Thus power is related to your own degree relative
  to your neighbors.
• There is a natural recursive definition similar
  to his Centrality measure.

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Discussion Topics

• T1 Centrality is a concept usually applied to
  undirected graphs, while prestige or status
  relates to the indegree of a node in a directed
  graph. What could outdegree represent? Could it
  be a useful measure?
• T2 List some networks you know, what might be
  usefully represented with a centrality measure,
  and which centrality measure would be most
  appropriate.