tokens: interaction with one galaxy twice as high than with all others) will be considered as bound ( F92 ). This is only valid in a statistical way and may be wrong for a particular galaxy. Ferguson ’s IP clearly does not take into account the cancellation of gravitational forces by different neighbors nor the three dimensional structure of the cluster. Also, the analysis of is always performed up to separations of , while according to the definition of in Eq. ( 5 )the ‚nearest neighbor’ of a galaxy might have a larger separation. We explore alternative IPs that take more than one influential neighbor into account. First, a substructure IP which compares the gravitational interaction for a galaxy with all its neighboring galaxies within () to the interaction with the rest of the cluster (, separations ): This IP should show a significantly higher fraction of galaxies with than Ferguson ’s IP. As a second variant we define a group IP by comparing the three most strongly interacting galaxies (if those galaxies are closer than , ) with the interaction by the rest of the cluster: where “” denotes that those maxima are only computed if the corresponding galaxies are located closer than to the th galaxy. This IP should be sensitive to the presence of subgroups within the cluster. We assume that if such subgroups exist, should show approximately the same values for the galaxies contained in a group. Therefore the number of galaxies with should range somewhere between the number of and . As hitherto only gravitational interaction is considered, a last IP is introduced which is sensitive to tidal interaction. It is almost the same IP as the one in Karachentsev (2005, hereafter Ka05) : The only difference is that in Ka05 a constant was added which allows to identify isolated galaxies (). 3.4.2. Direct position shuffling method The pseudo-clusters to calculate IPs which then can be compared with the real IPs based on the MA08 and WLG11 catalogs are created by a direct position shuffling. In this method the positions of two randomly chosen galaxies and are swapped directly. As in F92 this exchange is performed times where is the total number of galaxies in the sample. In this way it can happen that a galaxy changes its position several times in one run, while another may stay in place. 4. Results 4.1. Results for the <inline-formula specific-use="simple-math">Σ</inline-formula>(<italic>r</italic>)-analyses of the MA08 catalog The settings for the MC simulations analyzed in this section are given below. They are valid throughout this paper, unless mentioned otherwise. Primary-secondary discrimination at (74 giants and 399 possible companions at the outset). Primaries have to lie outside an ellipse with minor axis 250 kpc centered on the cluster center (45 primaries left). Distance to Coma: , , , , Distance modulus and therefore a scale of ( Adami et al. 2009 ). To calculate the absolute magnitudes, a small correction of is added to leading to a value of
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