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The first and last terms are normalized by a technique known as overlap coefficient [27].

Table 6 summarizes the edge and node overlap coefficient statistics among all pairs of topics for the two datasets.

Overlap coefficient considers two strings as a full match if one is a subset of the other [7].

The entry on row i, column j represents (R^{E}_{ij}(0.1)); the lower italic triangle represents edge overlap coefficient when (theta =0.3).

The entry on row i, column j represents (R^{E}_{ij}(0.1)); the lower italic triangle represents node overlap coefficient when (theta =0.1).

The entry on row i, column j represents (R^{V}_{ij}(0.5)); the lower italic triangle represents node overlap coefficient when (theta =5.0).

When user k transmits using rate, it introduces a bit overlap coefficient according to which the new rate is related to the nominal rate through the following: (1).

If (theta ) is small and the overlap coefficient is small, it means that the two topics are fairly separated in the network.

This method also calculates an overlap coefficient for each object in the TEM image that can be used to identify non-soot-aggregate structures.

For topics i and j, we define edge overlap coefficient as (R^{E}_{ij}(theta ) = frac{|tau _i(theta ) cap tau _j theta )|}{min {|tau _i(theta )|, |tau _j theta )|}}), and node overlap coefficient as ( R^{V}_{ij}(theta ) = frac{|nu _i(theta ) cap nu _j theta )|}{min {|nu _i(theta )|, |nu _j theta )|}}).

The overlap coefficient, also known as Simpson similarity, is a similarity measure related to the Jaccard index that computes the overlap between two sets, which is defined as Equation 10 ([Deza and Deza 2009]).

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