Modularity clustering is force-directed layout

By Andreas Noack. 2008

262 citations recorded by the source corpus.

Two natural and widely used representations for the community structure of networks are clusterings, which partition the vertex set into disjoint subsets, and layouts, which assign the vertices to positions in a metric space. This paper unifies prominent characterizations of layout quality and clustering quality, by showing that energy models of pairwise attraction and repulsion subsume Newman and Girvan's modularity measure. Layouts with optimal energy are relaxations of, and are thus consistent with, clusterings with optimal modularity, which is of practical relevance because the two representations are complementary and often used together.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics

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Citations in the corpus

ForceAtlas2, a Continuous Graph Layout Algorithm for Handy Network Visualization Designed for the Gephi Software (2014, background): “Noack [12] has shown that the proximities express communities.”
Community detection in graphs (2009, methodology): “…also allows to assess the stability of partitions (Massen and Doye, 2006) (Section XIV), it can be used to design layouts for graph visualization (Noack, 2009) and to perform a sort of renormalization of a graph, by transforming a graph into a smaller one with the same community structure…”
Comparing Community Structure to Characteristics in Online Collegiate Social Networks (2008, methodology): “An appealing feature (shown very recently) of detecting communities by maximizing modularity is that determining a network’s community structure in this way is equivalent to visualizing it using particular parameter values in a force-directed layout [ 78 ].”
ForceAtlas 2 , A Continuous Graph Layout Algorithm for Handy Network Visualization (2012, background): “Noack [3] has shown that the proximities express communities2.”
Systematic Literature Review on the Spread of Health-related Misinformation on Social Media (2019, methodology): “4 , the distance in the map between any pair of journals reflects their similarity to each other (van Eck and Waltman, 2010), and we use the LinLog/ modularity normalization technique to minimize the distance between connected nodes (Noack, 2009) .”
A Unifying Perspective on Neighbor Embeddings along the Attraction-Repulsion Spectrum (2020, background): “This is known as edge repulsion in the graph layout literature (Noack, 2007, 2009) and is important for embedding graphs that have nodes of very di ﬀ erent degrees.”
Quantifying Controversy in Social Media (2015, methodology): “edding This measure is based on a low-dimensional embedding of graphG produced by Gephi’s ForceAtlas2 algorithm [28] (the same algorithm used to produce the plots in Figures3and4). According to Noack [43], a force-directed embedding also maximizes modularity. Based on this observation, the twodimens”
A unified approach to mapping and clustering of bibliometric networks (2010, result): “The above result showing how mapping and clustering can be performed in a unified and consistent way resembles to some extent a result derived by Noack (2009).”