Social significance of community structure: statistical view

Community Detection Based on a Preferential Decision Model

The research on complex networks is a hot topic in many fields, among which community detection is a complex and meaningful process, which plays an important role in researching the characteristics of complex networks. Community structure is a common feature in the network. Given a graph, the process of uncovering its community structure is called community detection. Many community detection algorithms from different perspectives have been proposed. Achieving stable and accurate community division is still a non-trivial task due to the difficulty of setting specific parameters, high randomness and lack of ground-truth information. In this paper, we explore a new decision-making method through real-life communication and propose a preferential decision model based on dynamic relationships applied to dynamic systems. We apply this model to the label propagation algorithm and present a Community Detection based on Preferential Decision Model, called CDPD. This model intuitively aims to reveal the topological structure and the hierarchical structure between networks. By analyzing the structural characteristics of complex networks and mining the tightness between nodes, the priority of neighbor nodes is chosen to perform the required preferential decision, and finally the information in the system reaches a stable state. In the experiments, through the comparison of eight comparison algorithms, we verified the performance of CDPD in real-world networks and synthetic networks. The results show that CDPD not only has better performance than most recent algorithms on most datasets, but it is also more suitable for many community networks with ambiguous structure, especially sparse networks.

Network Evolution of a Large Online MSM Dating Community: 2005-2018

Due to multiple sexual partners and low rates of condom use, the HIV infection rate among MSM (men who have sex with men) is much higher than that of the general population. In order to analyze the characteristics of online activities of MSM, and to understand the evolution of their social networks, in this study we collect a comprehensive dataset, covering the period from January 2005 to June 2018, from the largest Chinese online community, Baidu Tieba. We build an online dating network for MSM-related individuals in the gay-bar community, and analyze the network from static and dynamic aspects. It is found that there is a strong homophily regarding the cities where users reside when developing interactions with others, and that most network measurements tend to be stable at the later stages of evolution, while the size of the largest community fluctuates. This is an indication that the network is formed of rapidly flexible interactions which changes quickly. In comparison with studies on heterosexual networks, we find that the MSM dating network shows differences in many aspects, such as the positive degree-degree correlation and high clustering coefficient, suggesting different thinking and measures should be taken in the policy making of public health management towards the MSM population.

Frequent pattern mining in multidimensional organizational networks

Network analysis can be applied to understand organizations based on patterns of communication, knowledge flows, trust, and the proximity of employees. A multidimensional organizational network was designed, and association rule mining of the edge labels applied to reveal how relationships, motivations, and perceptions determine each other in different scopes of activities and types of organizations. Frequent itemset-based similarity analysis of the nodes provides the opportunity to characterize typical roles in organizations and clusters of co-workers. A survey was designed to define 15 layers of the organizational network and demonstrate the applicability of the method in three companies. The novelty of our approach resides in the evaluation of people in organizations as frequent multidimensional patterns of multilayer networks. The results illustrate that the overlapping edges of the proposed multilayer network can be used to highlight the motivation and managerial capabilities of the leaders and to find similarly perceived key persons.

A Scheme to Design Community Detection Algorithms in Various Networks

Network structures, consisting of nodes and edges, have applications in almost all subjects. A set of nodes is called a community if the nodes have strong interrelations. Industries (including cell phone carriers and online social media companies) need community structures to allocate network resources and provide proper and accurate services. However, most detection algorithms are derived independently, which is arduous and even unnecessary. Although recent research shows that a general detection method that serves all purposes does not exist, we believe that there is some general procedure of deriving detection algorithms. In this paper, we represent such a general scheme. We mainly focus on two types of networks: transmission networks and similarity networks. We reduce them to a unified graph model, based on which we propose a method to define and detect community structures. Finally, we also give a demonstration to show how our design scheme works.

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.

Subnormal Distribution Derived From Evolving Networks With Variable Elements

During the past decades, power-law distributions have played a significant role in analyzing the topology of scale-free networks. However, in the observation of degree distributions in practical networks and other nonuniform distributions such as the wealth distribution, we discover that, there exists a peak at the beginning of most real distributions, which cannot be accurately described by a monotonic decreasing power-law distribution. To better describe the real distributions, in this paper, we propose a subnormal distribution derived from evolving networks with variable elements and study its statistical properties for the first time. By utilizing this distribution, we can precisely describe those distributions commonly existing in the real world, e.g., distributions of degree in social networks and personal wealth. Additionally, we fit connectivity in evolving networks and the data observed in the real world by the proposed subnormal distribution, resulting in a better performance of fitness.

An application of the Shapley value to the analysis of co-expression networks

We study the problem of identifying relevant genes in a co-expression network using a (cooperative) game theoretic approach. The Shapley value of a cooperative game is used to asses the relevance of each gene in interaction with the others, and to stress the role of nodes in the periphery of a co-expression network for the regulation of complex biological pathways of interest. An application of the method to the analysis of gene expression data from microarrays is presented, as well as a comparison with classical centrality indices. Finally, making further assumptions about the a priori importance of genes, we combine the game theoretic model with other techniques from cluster analysis.

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.

Analysis of epidemic spreading process in multi-communities

In practice, an epidemic might be spreading among multi-communities; while the communities are usually intra-connected. In this manuscript, each community is modeled as a multiplex network (i.e., virtual layer and physical one). The connections inside certain community are referred as inter-contacts while the intra-contacts denote the connections among communities. For the epidemic spreading process, the traditional susceptible-infected-recovered (SIR) model is adopted. Then, corresponding state transition trees are determined and simulations are conducted to study the epidemic spreading process in multi-communities. Here, the effect of incorporating virtual layer on the range of individual affected by the epidemic is pursued. As illustrated, multi-summits are incurred if the spreading in multi-communities is considered; furthermore, the disparity between summits varies. This is affected by various factors. As indicated, the incorporation of virtual layer is capable of reducing the proportion of individuals being affected; moreover, disparity of different summits is likely to be increased regarding with scenarios of excluding virtual layer. Furthermore, the summit is likely to be postponed if virtual layer is incorporated.