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**NETWORK > CENTRALITY >POLITICAL INDEPENDENCE (LBK)**

**PURPOSE **Calculates the political indepencence or LBK power centrality scores of a valued network.

**DESCRIPTION **The political independence or LBK power centrality is a point scoring system based loosely on ideas from exchange theory. Each actor gains opportunities and power from those to whom they are directly connected. If these actors have alternatives then the power derived from the connections is diminshed, but it is then increased if the alternates have other connections. This continues propagating through the whole network but the effect decreases he furtther away the connections are. In addition the routine has the facility to include an effect derived from a group partition so that out-group connections have a bigger effect than in-group connections. Hence actors that are an odd distance away contribute positively to the centrality score and actors that are an even distance away contribute negatively. For a given actor x the points system is described as follows. There are two user defined factors, disattenuation and outgroup discount. The factors apply to the weighted edges where any edge that connects out of xs group is weighted by the outgroup discount. For any edge let d be the distance from the closest endpoint to x, then provided d is less than the prescribed maimum distance the edge is weighted by a factor equal to the disattenuation raised to the power d-1. If d is even the edge is multiplied by -1. The LBK power score is half the sum of all the elements in the weighted matrix formed in this way.

**PARAMETERS**

**Weighted Tie Network:**

** **Name of file containing network to be analyzed. Data type: Valued Graph

**Attribute Dataset:**

Optional file contating attribute data which column of the data contains the relevan attribute should be specified this data should be categorical and partition the data. If this is left blank than the outgroup discount is not applied

**Output Scores: **(Default=<inputfilename>-LBK)

Name of UCINET file contating centrality results.

**DisAttenuation **(Default=0.8)

Attenuation factor equals the amount of decrease in influence an actor has the further away they are from the actor whose centrality is calculated.

**Max Distance**

** **Actors at a value greater than the max distance do not affect the points score.

**Outgroup Discount**

** **The amount of reduction applied to an edge that spans out of the actor whose centrality is being calculated group.

**Include diagnostics**

Ticking this gives the weighted matrix for each actor.

** **

**LOG FILE **The points tally for each actor. If the diagnostic box has been ticked the related matrix for each actor is given. The centrality scores are half the sum of all the edges within each matrix.

**TIMING** O(N^3).

**COMMENTS **

**REFERENCES**