Simmelian backbone extraction

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This transformation algorithm is meant to make network data more easy to visualize and analyze, in particular with regard to detecting underlying community structures. The method is based on local ranking and overlap calculations to extract a Simmelian backbone of strong and redundant ties. More detailed background information is provided in

For questions and comments, or if you want to apply the concept to big data, please contact Bobo Nick.

Contents

Where to find

Access is given via the transformation tab in the left-hand side of the visone window: set level to network and operation to Simmelian backbone.

Simmelian-backbone-find.png

Configuration

Ranking calculation

The Simmelian backbone is extracted from a ranked neighborhood graph. For this purpose, each undirected edge is split into two contrary directed edges, and the algorithm will rank each node's (outgoing) neighbors according to an associated (ordinal) link strength attribute:

Neighbors with equal link strength are equally ranked with the best available rank. The resulting neighborhood rankings are saved in a link attribute termed ranking. (For technical reasons, if the selected link strength attribute is termed ranking or redundancy it will be renamed into backbone-weight (ranking) or backbone-weight (redundancy), respectively.)

Simmelian-backbone-config.png

Redundancy assessment

Next, for designated pairs of nodes, the algorithm will calculate the redundancy of top-ranked neighbors. Always, each redundancy assessment is associated with a directed link (from ego to alter) in the ranked neighborhood graph. The resulting redundancy values are saved in a link attribute termed redundancy.

Parametric variant

If parametric is selected (default), the required redundancy for a link to be included in the Simmelian backbone is specified in terms of a necessary number of top-ranked common neighbors (regarding ego and alter associated with this link):

Special cases: If conditioned is true, non-top-ranked links will have undefined overlap values. Setting min overlap to zero will imply that only links with undefined overlap value are removed from the network.

Non-parametric variant

In the non-parametric variant of the transformation algorithm, a redundancy calculation is triggered for each link in the ranked neighborhood graph. The redundancy is defined as the maximum (ranked) Jaccard coefficient that is found when iteratively comparing top ranked neighbors (including more and more ranks). For a link to be included in the Simmelian backbone, the best found Jaccard coefficient has to be at least one half.

Reciprocity handling

For any of the two variants (parametric, or non-parametric redundancy assessment), you can decide whether ego is identified with alter in the redundancy calculations, i.e. reciprocity within top ranks is counted as overlap (default), or whether ego's rank in alter's neighborhood and alter's rank in ego's neighborhood are not taken into account in the redundancy assessment.

Result

For convenience, if layout is selected, visone's quick layout functionality is used to visualize the modified network structure at the end of the algorithm; otherwise, all node positions remain as before.

Simmelian-backbone-result.png

Use apply to to select the network(s) for which the calculations shall be performed. Since the network structure is altered by the algorithm, result in a new network rather than this network is proposed as default. The calculation is triggered by clicking the transform button at the bottom.

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