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In this paper we introduce an integrative network module determination method family, called ModuLand (see Box 1 for the glossary of novel terms).
This module determination method family is based on the novel concept of understanding the overlapping modules as hills of an influence function-based, centrality-type community landscape.
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As the members of the karate club have split into two factions later, the network became a gold-standard of module determination methods [1] [5], [7].
Numerous module determination methods are based on the intuitive picture identifying the network communities as dense groups of the network, whose nodes have a much stronger influence on each other than on the rest of the network.
TotalHill method: a local maxima-based module determination approach, in which the module membership value of a link is determined by all the module membership values of its neighboring links (see Sections V.2.c. and V.2.d. in the Electronic Supplementary Material S1).
GradientHill method: a local maxima-based module determination approach, in which the module membership value of a link is determined by the module membership value(s) only of its neighboring link(s) having maximal centrality values (see Section V.2.b. in the Electronic Supplementary Material S1).
ProportionalHill method: a local maxima-based module determination approach, in which the module membership value of a link is determined by the module membership values only of its neighboring links having non lower centrality values (see main text and Section V.2.b. in the Electronic Supplementary Material S1).
ModuLand method family: the integrative name of our module determination approach based on the hills of the community landscape (see main text and Section II. in the Electronic Supplementary Material S1).
Additionally, former methods yielding non-overlapping modules (which can be interpreted as the application of the threshold-based hill determination method) can be upgraded to overlapping modularization methods using the local maxima-based module determination approach of the ModuLand method family (for details see Section IV.4. in the Electronic Supplementary Material S1).
We examine the robustness of the modular partitioning with respect to the method used for detecting communities by using another module determination algorithm [40].
A module can also be divided two sub-module by the signs of d ij and the sub-module is determined using a similar approach to the module determination.
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