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These steps are repeated iteratively until a maximum of modularity is attained and a hierarchy of communities is produced.

This process is applied until modularity cannot be increased and a local maximum of modularity is achieved.

These steps are repeated iteratively until a maximum of modularity is reached.

Although the partitioning seems like an approximate method and nothing ensures that the global maximum of modularity is attained, several tests have shown that it provides a decomposition in communities with modularity that is close to optimality [ 25].

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Second, the solution obtained in the first stage is improved through an iterative optimisation procedure employing a model that we have developed previously and was proven efficient in detecting communities in small to medium size networks through a global maximum of the modularity metric (OptMod, [ 30]).

Effective modularity is the difference between the maximum modularity of the graph and the average maximum modularity of a number of random graphs [ 38].

The merge process is complete when one of the following conditions is met: 1) maximum modularity, 2) maximum size, or 3) maximum module score (Section Weights and significance scoring).

The maximum modularities of non-directed customer-supplier, non-directed licensor-licensee, and strategic alliance networks over the entire sample period are 0.64, 0.75, and 0.74, respectively.

As recommended in [19], we extended the JUNG implementation to sequentially remove all edges, and recalculate the network modularity after each edge removal, and automatically identify the number of edges which results in the optimal / maximum network modularity.

However, P IN / P T peaked at ~5% and had a maximum value of ~25%, implying that none of the literature defined pathways met the simplest definition of modularity (P IN / P T  < 0.5).

Most authors seem to equate this issue with the one of finding the maximum value of the modularity, as defined by Newman.

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