absorbing random-walk centrality - boston university · absorbing random-walk centrality theory...

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)

2

Centrality measures

TeamDegree ClosenessBetweennessFlow betweenness

Single nodeDegree Closeness Betweenness Random walk

RW betweennessFlow betweennessInformation centralityPageRank

3

Centrality measures

TeamDegree ClosenessBetweennessFlow betweenness

Single nodeDegree Closeness Betweenness Random walk

RW betweennessFlow betweennessInformation centralityPageRank

Our work

4

Random walk centralityFor a single node ,

with respect to the whole graph ,

measuring the expected time to reach node .

v

G = (V, E)

v

5

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}

6

Finding the best teamProperties

‣ NP-hard

‣ Monotone

‣ Supermodular

Greedy algorithm

‣ complexity , : graph nodes : team size

‣ approximation guarantee

�O(kn3)

�1 � 1

e

�

nk

7

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.

8

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)

9