absorbing random-walk centrality - boston university · absorbing random-walk centrality theory...
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C. Mavroforakis, M. Mathioudakis, A. Gionis
Absorbing random-walk centralityTheory & Algorithms
New node centrality measure:
‣ Defined on sets of nodes (teams)
‣ Generalization of random walk centrality
‣ Important team = central + diverse
‣ Query nodes
‣ Code available on GitHub (absorbing-centrality)
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Centrality measures
TeamDegree ClosenessBetweennessFlow betweenness
Single nodeDegree Closeness Betweenness Random walk
RW betweennessFlow betweennessInformation centralityPageRank
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Centrality measures
TeamDegree ClosenessBetweennessFlow betweenness
Single nodeDegree Closeness Betweenness Random walk
RW betweennessFlow betweennessInformation centralityPageRank
Our work
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Random walk centralityFor a single node ,
with respect to the whole graph ,
measuring the expected time to reach node .
v
G = (V, E)
v
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Absorbing rw. centralityFor a set of nodes ,
with respect to a subset of nodes ,
measuring the expected time to reach any node in
3-team1-team
{vi}
Q � V
{vi}
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Finding the best teamProperties
‣ NP-hard
‣ Monotone
‣ Supermodular
Greedy algorithm
‣ complexity , : graph nodes : team size
‣ approximation guarantee
�O(kn3)
�1 � 1
e
�
nk
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Quality of solutionDataset: les misérables (70 nodes)
Top- ranked with: ‣ Degree centrality ‣ Closeness centrality ‣ Personalized PageRank
Greedy outperforms the heuristics.
Personalized PageRank is a good and fast alternative.
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k
New node centrality measure:
‣ Defined on sets of nodes (teams)
‣ Generalization of random walk centrality
‣ Important team = central + diverse
‣ Query nodes
‣ Code available on GitHub (absorbing-centrality)
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