Recently, a type of multi-resolution methods in community detection wasintroduced, which can adjust the resolution of modularity by modifying themodularity function with tunable resolution parameters, such as those proposedby Arenas, Fernandez and Gomez and by Reichardt and Bornholdt. In this paper,we show that these methods still have the intrinsic limitation-largecommunities may have been split before small communities become visible-becauseit is at the cost of the community stability that the enhancement of themodularity resolution is obtained. The theoretical results indicated that thelimitation depends on the degree of interconnectedness of small communities andthe difference between the sizes of small communities and of large communities,while independent of the size of the whole network. These findings have beenconfirmed in several example networks, where communities even arefull-completed sub-graphs.
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