Related papers: Modularity clustering is force-directed layout
In this paper we discuss some problematic aspects of Newman's modularity function QN. Given a graph G, the modularity of G can be written as QN = Qf -Q0, where Qf is the intracluster edge fraction of G and Q0 is the expected intracluster…
Neural network representations contain structure beyond what was present in the training labels. For instance, representations of images that are visually or semantically similar tend to lie closer to each other than to dissimilar images,…
Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to…
Clusters appear in nature in a diversity of contexts, involving distances as long as the cosmological ones, and down to atoms and molecules and the very small nuclear size. They also appear in several other scenarios, in particular in…
Graph clustering (or community detection) has long drawn enormous attention from the research on web mining and information networks. Recent literature on this topic has reached a consensus that node contents and link structures should be…
The clustering coefficient is a valuable tool for understanding the structure of complex networks. It is widely used to analyze social networks, biological networks, and other complex systems. While there is generally a single common…
Modularity, first proposed by [Newman and Girvan, 2004], is one of the most popular ways to quantify the significance of community structure in complex networks. It can serve as both a standard benchmark to compare different community…
Grid visualizations are widely used in many applications to visually explain a set of data and their proximity relationships. However, existing layout methods face difficulties when dealing with the inherent cluster structures within the…
Community structures are an important feature of many social, biological and technological networks. Here we study a variation on the method for detecting such communities proposed by Girvan and Newman and based on the idea of using…
Modularity is widely used to effectively measure the strength of the disjoint community structure found by community detection algorithms. Several overlapping extensions of modularity were proposed to measure the quality of overlapping…
The issue of partitioning a network into communities has attracted a great deal of attention recently. Most authors seem to equate this issue with the one of finding the maximum value of the modularity, as defined by Newman. Since the…
Motivated by questions in biological classification, we discuss some elementary combinatorial and computational properties of certain set systems that generalize hierarchies, namely, 'patchworks', 'weak patchworks', 'ample patchworks' and…
Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced…
Coordination games are important to explain efficient and desirable social behavior. Here we study these games by extensive numerical simulation on networked social structures using an evolutionary approach. We show that local network…
We introduce a simple model of active transport for an ensemble of particles driven by an external shear flow. Active refers to the fact that the flow of the particles is modified by the distribution of particles itself. The model consists…
A new fast algorithm for clustering and classification of large collections of text documents is introduced. The new algorithm employs the bipartite graph that realizes the word-document matrix of the collection. Namely, the modularity of…
We show here that the problem of maximizing a family of quantitative functions, encompassing both the modularity (Q-measure) and modularity density (D-measure), for community detection can be uniformly understood as a combinatoric…
One of the most prominent challenges in clustering is "the user's dilemma," which is the problem of selecting an appropriate clustering algorithm for a specific task. A formal approach for addressing this problem relies on the…
Emergent design failures are ubiquitous in complex systems, and often arise when system elements cluster. Approaches to systematically reduce clustering could improve a design's resilience, but reducing clustering is difficult if it is…
The generalized version of modularity for multilayer networks, a.k.a. multislice modularity, is characterized by two model parameters, namely resolution factor and inter-layer coupling factor. The former corresponds to a notion of…