Potts model based on a Markov process computation solves the community structure problem effectively

A community partitioning algorithm for cyberspace

Community partitioning is an effective technique for cyberspace mapping. However, existing community partitioning algorithm only uses the topological structure of the network to divide the community and disregards factors such as real hierarchy, overlap, and directionality of information transmission between communities in cyberspace. Consequently, the traditional community division algorithm is not suitable for dividing cyberspace resources effectively. Based on cyberspace community structure characteristics, this study introduces an algorithm that combines an improved local fitness maximization (LFM) algorithm with the PageRank (PR) algorithm for community partitioning on cyberspace resources, called PR-LFM. First, seed nodes are determined using degree centrality, followed by local community expansion. Nodes belonging to multiple communities undergo further partitioning so that they are retained in the community where they are most important, thus preserving the community's original structure. The experimental data demonstrate good results in the resource division of cyberspace.

Statistics of geometric clusters in Potts model: statistical mechanics approach

The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters' size distributions is developed. It allows full description of percolation transition when a giant cluster of equal-valued Potts spins appears. The method is applied to the short-ranged q-state ferromagnetic Potts model on the Bethe lattices with the arbitrary coordination number z . The analytical results for the field-temperature percolation phase diagram of geometric spin clusters and their size distribution are obtained. The last appears to be proportional to that of the classical non-correlated bond percolation with the bond probability, which depends on temperature and Potts model parameters.

Critical analysis of (Quasi-)Surprise for community detection in complex networks

Module or community structures widely exist in complex networks, and optimizing statistical measures is one of the most popular approaches for revealing and identifying such structures in real-world applications. In this paper, we focus on critical behaviors of (Quasi-)Surprise, a type of statistical measure of interest for community structure, accompanied by a series of comparisons with other measures. Specially, the effect of various network parameters on the measures is thoroughly investigated. The critical number of dense subgraphs in partition transition is derived, and a kind of phase diagrams is provided to display and compare the phase transitions of the measures. The effect of “potential well” for (Quasi-)Surprise is revealed, which may be difficult to get across by general greedy (agglomerative or divisive) algorithms. Finally, an extension of Quasi-Surprise is introduced for the study of multi-scale structures. Experimental results are of help for understanding the critical behaviors of (Quasi-)Surprise, and may provide useful insight for the design of effective tools for community detection.

Quantum transport senses community structure in networks

Quantum time evolution exhibits rich physics, attributable to the interplay between the density and phase of a wave function. However, unlike classical heat diffusion, the wave nature of quantum mechanics has not yet been extensively explored in modern data analysis. We propose that the Laplace transform of quantum transport (QT) can be used to construct an ensemble of maps from a given complex network to a circle S^{1}, such that closely related nodes on the network are grouped into sharply concentrated clusters on S^{1}. The resulting QT clustering (QTC) algorithm is as powerful as the state-of-the-art spectral clustering in discerning complex geometric patterns and more robust when clusters show strong density variations or heterogeneity in size. The observed phenomenon of QTC can be interpreted as a collective behavior of the microscopic nodes that evolve as macroscopic cluster "orbitals" in an effective tight-binding model recapitulating the network. python source code implementing the algorithm and examples are available at https://github.com/jssong-lab/QTC.

The Odyssey's mythological network

In this work, we study the mythological network of Odyssey of Homer. We use ordinary statistical quantifiers in order to classify the network as real or fictional. We also introduce an analysis of communities which allows us to see how network properties shall emerge. We found that Odyssey can be classified both as real and fictional network. This statement is supported as far as mythological characters are removed, which results in a network with real properties. The community analysis indicated to us that there is a power-law relationship based on the max degree of each community. These results allow us to conclude that Odyssey might be an amalgam of myth and of historical facts, with communities playing a central role.

Emergent community agglomeration from data set geometry

In the statistical learning language, samples are snapshots of random vectors drawn from some unknown distribution. Such vectors usually reside in a high-dimensional Euclidean space, and thus the "curse of dimensionality" often undermines the power of learning methods, including community detection and clustering algorithms, that rely on Euclidean geometry. This paper presents the idea of effective dissimilarity transformation (EDT) on empirical dissimilarity hyperspheres and studies its effects using synthetic and gene expression data sets. Iterating the EDT turns a static data distribution into a dynamical process purely driven by the empirical data set geometry and adaptively ameliorates the curse of dimensionality, partly through changing the topology of a Euclidean feature space R^{n} into a compact hypersphere S^{n}. The EDT often improves the performance of hierarchical clustering via the automatic grouping information emerging from global interactions of data points. The EDT is not restricted to hierarchical clustering, and other learning methods based on pairwise dissimilarity should also benefit from the many desirable properties of EDT.

Social significance of community structure: statistical view

Community structure analysis is a powerful tool for social networks that can simplify their topological and functional analysis considerably. However, since community detection methods have random factors and real social networks obtained from complex systems always contain error edges, evaluating the significance of a partitioned community structure is an urgent and important question. In this paper, integrating the specific characteristics of real society, we present a framework to analyze the significance of a social community. The dynamics of social interactions are modeled by identifying social leaders and corresponding hierarchical structures. Instead of a direct comparison with the average outcome of a random model, we compute the similarity of a given node with the leader by the number of common neighbors. To determine the membership vector, an efficient community detection algorithm is proposed based on the position of the nodes and their corresponding leaders. Then, using a log-likelihood score, the tightness of the community can be derived. Based on the distribution of community tightness, we establish a connection between p-value theory and network analysis, and then we obtain a significance measure of statistical form . Finally, the framework is applied to both benchmark networks and real social networks. Experimental results show that our work can be used in many fields, such as determining the optimal number of communities, analyzing the social significance of a given community, comparing the performance among various algorithms, etc.