Resolution limit in community detection

By Santo Fortunato, Marc Barthelemy. Proceedings of the National Academy of Sciences of the United States of America, 2006

3,037 citations recorded by the source corpus.

Detecting community structure is fundamental for uncovering the links between structure and function in complex networks and for practical applications in many disciplines such as biology and sociology. A popular method now widely used relies on the optimization of a quantity called modularity, which is a quality index for a partition of a network into communities. We find that modularity optimization may fail to identify modules smaller than a scale which depends on the total size of the network and on the degree of interconnectedness of the modules, even in cases where modules are unambiguously defined. This finding is confirmed through several examples, both in artificial and in real social, biological, and technological networks, where we show that modularity optimization indeed does not resolve a large number of modules. A check of the modules obtained through modularity optimization is thus necessary, and we provide here key elements for the assessment of the reliability of this community detection method.

Subfields: Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/39433dcfe25535df4398742432f2fb11330b0097

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Citations in the corpus

Generalized Louvain method for community detection in large networks (2011, background): “Values obtained put into evidence that our strategy performs fair good results, avoiding the well-known effect due to the resolution limit of the modularity optimization [18].”
Defining and evaluating network communities based on ground-truth (2012, background): “Identifying such communities in networks [14], [6], [26], [9] has proven to be a challenging task [10], [18], [17] due to three reasons: There exist multiple structural deﬁnitions of network communities [5], [24]; Even if we would agree on a single common structural deﬁnition ( i.e. , a single…”
The Physics of Communicability in Complex Networks (2011, background): “The detection of communities in complex networks has become one of the most intensive areas of interdisciplinary research in this field (Fortunato, 2010; Fortunato and Barthélemy, 2007; Newman, 2004; 2006a; b; von Luxburg, 2007).”
Citation-based clustering of publications using CitNetExplorer and VOSviewer (2017, background): “The modularity function suffers from a problem known as the resolution limit (Fortunato & Barthélemy, 2007).”
The community-search problem and how to plan a successful cocktail party (2010, methodology): “There are many papers studying the modularity measure and developing algorithms for it, for instance, Brandes et al. [6] showed that it is NP-hard to optimize modularity, Fortunato and Barthelemy [14] identify the resolution-limit problem, White and Smyth [29] follow a spectral approach to optimize ”
Modular Brain Networks (2015, background): “This problem is called the resolution limit of modularity (Fortunato & Barthelemy 2007) and arises from a trade-off between the number of communities into which a network is partitioned and the Q value associated with those partitions.”
Extending the definition of modularity to directed graphs with overlapping communities (2008, background): “While an important resolution limit of the modularity measure has been pointed out by Fortunato and Barthelemy in [7], the modularity seems nevertheless to be a useful measure of community structures, and many algorithms for ﬁnding graph partitions which give optimal modularity have been proposed…”
Nine quick tips for analyzing network data (2019, background): “For instance, modularity, number of modules, and network size are known to be intertwined [28].”
Clustering and Community Detection in Directed Networks: A Survey (2013, background): “However, as noted by Fortunato and Barthélemy [49], modularity suffers from the so-called resolution limit.”
Finding Statistically Significant Communities in Networks (2010, neutral): “This is the same null model adopted in modularity optimization [63], and is responsible for the serious problems of this technique, like its well known resolution limit [64].”
Overlapping community detection in networks: The state-of-the-art and comparative study (2011, background): “e relative to the null model. However, modularity (including the extended variants) should always be used with caution due to the resolution limit beyond which no community structure can be detected [Fortunato and Barthelemy 2007]. Moreover, the complexity of the modularity landscape suggests that a”
Uncovering space-independent communities in spatial networks (2010, methodology): “These methods have been shown to produce useful and relevant partitions in a broad class of systems [31], even if modularity suﬀers from limitations such as resolution limit [65] and a possible high degeneracy of its landscape [66, 67].”