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Given an optimal clique-colouration ofG′, an optimal clique-colouration ofGis obtained assigning to every vertex belonging to a maximal strong module ofGthe same colour of its representative vertex inG′.
We say that M is a strong module if for any other module A the intersection M∩A is empty or equals either M or A. For a non-trivial graph G, the family {M1,M2,…,M p } of all maximal (proper) strong modules is a partition of V(G).
Lastly, all landmarks were grouped into two bins, based on membership in a "strong" module or a "weak" module, and a Mann-Whitney test was used to test for differences in landmark variances between the two bins.
In Carnivora, the molar group had marginally significantly higher disparity than the random sets of "weak" module landmarks (p = 0.05), while the orbit, zygomatic-pterygoid, and vault groups all had significantly or marginally significantly higher disparity than the random sets of "strong" module landmarks (p<0.001, p<0.001, and p = 0.03, respectively).
In a strong module each vertex has more connections with the cluster than with the rest of the graph.
In PPI networks, there exist complexes which have structure of a strong module, or of a weak module, or a combination of the two.
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For disconnected G, the maximal strong modules are the connected components.
If (overline{G}) is disconnected, the maximal strong modules of G are the connected components of (overline{G}).
Let {M1,M2,…,M p } be the family of all maximal (proper) strong modules of G and let {v1,…2,v,v p } be the set of the corresponding characteristic vertices in G′.
In contrast, the facilitation hypothesis predicts that strong modules show display high morphological disparity.
The constraint hypothesis predicts that "strong" modules, sets of highly-correlated traits, should display low morphological disparity.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com