# Improving Estimation of Betweenness Centrality for Scale-Free Graphs

## Abstract

Betweenness centrality is a graph statistic used to nd vertices that are participants in a large number of shortest paths in a graph. This centrality measure is commonly used in path and network interdiction problems and its complete form requires the calculation of all-pairs shortest paths for each vertex. This leads to a time complexity of O(jV jjEj), which is impractical for large graphs. Estimation of betweenness centrality has focused on performing shortest-path calculations on a subset of randomly- selected vertices. This reduces the complexity of the centrality estimation to O(jSjjEj); jSj < jV j, which can be scaled appropriately based on the computing resources available. An estimation strategy that uses random selection of vertices for seed selection is fast and simple to implement, but may not provide optimal estimation of betweenness centrality when the number of samples is constrained. Our experimentation has identi ed a number of alternate seed-selection strategies that provide lower error than random selection in common scale-free graphs. These strategies are discussed and experimental results are presented.

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1409962

- Report Number(s):
- LLNL-TR-741432

- DOE Contract Number:
- AC52-07NA27344

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Bromberger, Seth A., Klymko, Christine F., Henderson, Keith A., Pearce, Roger, and Sanders, Geoff.
```*Improving Estimation of Betweenness Centrality for Scale-Free Graphs*. United States: N. p., 2017.
Web. doi:10.2172/1409962.

```
Bromberger, Seth A., Klymko, Christine F., Henderson, Keith A., Pearce, Roger, & Sanders, Geoff.
```*Improving Estimation of Betweenness Centrality for Scale-Free Graphs*. United States. doi:10.2172/1409962.

```
Bromberger, Seth A., Klymko, Christine F., Henderson, Keith A., Pearce, Roger, and Sanders, Geoff. Tue .
"Improving Estimation of Betweenness Centrality for Scale-Free Graphs". United States. doi:10.2172/1409962. https://www.osti.gov/servlets/purl/1409962.
```

```
@article{osti_1409962,
```

title = {Improving Estimation of Betweenness Centrality for Scale-Free Graphs},

author = {Bromberger, Seth A. and Klymko, Christine F. and Henderson, Keith A. and Pearce, Roger and Sanders, Geoff},

abstractNote = {Betweenness centrality is a graph statistic used to nd vertices that are participants in a large number of shortest paths in a graph. This centrality measure is commonly used in path and network interdiction problems and its complete form requires the calculation of all-pairs shortest paths for each vertex. This leads to a time complexity of O(jV jjEj), which is impractical for large graphs. Estimation of betweenness centrality has focused on performing shortest-path calculations on a subset of randomly- selected vertices. This reduces the complexity of the centrality estimation to O(jSjjEj); jSj < jV j, which can be scaled appropriately based on the computing resources available. An estimation strategy that uses random selection of vertices for seed selection is fast and simple to implement, but may not provide optimal estimation of betweenness centrality when the number of samples is constrained. Our experimentation has identi ed a number of alternate seed-selection strategies that provide lower error than random selection in common scale-free graphs. These strategies are discussed and experimental results are presented.},

doi = {10.2172/1409962},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Nov 07 00:00:00 EST 2017},

month = {Tue Nov 07 00:00:00 EST 2017}

}