# Difference between revisions of "Backbone Layout"

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+ | === Asymptotic Complexity === | ||

+ | The computation of the embeddedness together with the backbone extraction takes <math> O(|E| \triangle(G))</math> steps for a graph <math>G=(V,E)</math> where <math>\triangle(G)</math> is the maximum degree of a vertex <math> v\in V</math>. This scales very well for large networks with, e.g., millions of edges and nodes. | ||

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+ | The final layout based on the extracted backbone needs <math>O(|V|^2</math> time and memory, which does not scale for large graphs. |

## Revision as of 13:19, 25 August 2014

Small-world graphs have characteristically low average distance and thus cause force-directed methods to generate drawings that look like hairballs.

The backbone layout tries to untangle hairball graphs. The method is based on a spanning subgraph that is sparse but connected and consists of strong ties holding together communities.

Strong ties are identified using a measure of embeddedness which is based on a weighted accumulation of triangles in quadrangles.

More detailed background information is provided in

- Arlind Nocaj, Mark Ortmann, and Ulrik Brandes: Untangling Hairballs: From 3 to 14 Degrees of Separation, to appear in Proceedings of the 22nd International Symposium on Graph Drawing (GD 2014).

### Asymptotic Complexity

The computation of the embeddedness together with the backbone extraction takes steps for a graph where is the maximum degree of a vertex . This scales very well for large networks with, e.g., millions of edges and nodes.

The final layout based on the extracted backbone needs time and memory, which does not scale for large graphs.