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**1 - 5**of**5**### Axioms for graph clustering quality functions

"... We investigate properties that intuitively ought to be satisfied by graph clustering quality functions, i.e. functions that assign a score to a clustering of a graph. Graph clustering, also known as network community detection, is often performed by optimizing such a function. Two axioms tailored fo ..."

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We investigate properties that intuitively ought to be satisfied by graph clustering quality functions, i.e. functions that assign a score to a clustering of a graph. Graph clustering, also known as network community detection, is often performed by optimizing such a function. Two axioms tailored for graph clustering quality functions are introduced, and the four axioms introduced in previous work on distance based clustering are reformulated and generalized for the graph setting. We show that modularity, a standard quality function for graph clustering, does not satisfy all of these six properties. This motivates the derivation of a new family of quality functions, adaptive scale modularity, which does satisfy the proposed axioms. Adaptive scale modularity has two parameters, which give greater flexibility in the kinds of clusterings that can be found. Standard graph clustering quality functions, such as normalized cut and unnormalized cut, are obtained as special cases of adaptive scale modularity. In general, the results of our investigation indicate that the considered axiomatic frame-work covers existing ‘good ’ quality functions for graph clustering, and can be used to derive an interesting new family of quality functions.

### Hierarchical Quasi-Clustering Methods for Asymmetric Networks

"... This paper introduces hierarchical quasi-clustering methods, a generalization of hierar-chical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data. We show that this output structure is equivalent to a finite quasi-ultrametric space and study admis ..."

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This paper introduces hierarchical quasi-clustering methods, a generalization of hierar-chical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data. We show that this output structure is equivalent to a finite quasi-ultrametric space and study admissibility with respect to two desirable properties. We prove that a modified version of single linkage is the only admis-sible quasi-clustering method. Moreover, we show stability of the proposed method and we establish invariance properties fulfilled by it. Algorithms are further developed and the value of quasi-clustering analysis is illustrated with a study of internal migration within United States. 1.

### Axioms for graph clustering quality functions Axioms for graph clustering quality functions

"... We investigate properties that intuitively ought to be satisfied by graph clustering quality functions, i.e. functions that assign a score to a clustering of a graph. Graph clustering, also known as network community detection, is often performed by optimizing such a function. Two axioms tailored fo ..."

Abstract
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We investigate properties that intuitively ought to be satisfied by graph clustering quality functions, i.e. functions that assign a score to a clustering of a graph. Graph clustering, also known as network community detection, is often performed by optimizing such a function. Two axioms tailored for graph clustering quality functions are introduced, and the four axioms introduced in previous work on distance based clustering are reformulated and generalized for the graph setting. We show that modularity, a standard quality function for graph clustering, does not satisfy all of these six properties. This motivates the derivation of a new family of quality functions, adaptive scale modularity, which does satisfy the proposed axioms. Adaptive scale modularity has two parameters, which give greater flexibility in the kinds of clusterings that can be found. Standard graph clustering quality functions, such as normalized cut and unnormalized cut, are obtained as special cases of adaptive scale modularity. In general, the results of our investigation indicate that the considered axiomatic frame-work covers existing ‘good ’ quality functions for graph clustering, and can be used to derive an interesting new family of quality functions.

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"... Please be advised that this information was generated on 2016-03-05 and may be subject to change. Axioms for graph clustering quality functions Axioms for graph clustering quality functions ..."

Abstract
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Please be advised that this information was generated on 2016-03-05 and may be subject to change. Axioms for graph clustering quality functions Axioms for graph clustering quality functions