Social networks contain implicit knowledge that can be used to infer hierarchical relations that are not explicitly present in the available data. Interaction patterns are typically affected by use ...
More recently, @cite_15 argue that not only the sign and strength are important when it comes to obtaining a better understanding of social network structure, but also the direction of the ties between the actors. Liebowitz @cite_10 integrates the usage of an analytical hierarchical process with social network analysis on the organizational level to create a knowledge map. Moreover, @cite_16 adopt the principle of social stratification in their approach, which refers to the categorization of people in society into ranked groups based on their status, power, wealth or knowledge. By applying stratification on humans, they assumed that people who are higher up in the hierarchy tend to have a higher status (ranking) in comparison to people who are lower in the hierarchy. Further, people at the top levels of the hierarchy are less likely to connect to people at low levels of the hierarchy. An algorithm has been suggested to find the best hierarchy in a directed network. However, they have not considered the time dimension in the problem. Moreover, they study the problem at a network-level and not at an actor-level as in this study.
@cite_15 @cite_16 @cite_10
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Trust networks, where people leave trust and distrust feedback, are becoming increasingly common. These networks may be regarded as signed graphs, where a positive edge weight captures the degree of trust while a negative edge weight captures the degree of distrust. Analysis of such signed networks has become an increasingly important research topic. One important analysis task is that of sign inference, i.e., infer unknown (or future) trust or distrust relationships given a partially observed signed network. Most state-of-the-art approaches consider the notion of structural balance in signed networks, building inference algorithms based on information about links, triads, and cycles in the network. In this paper, we first show that the notion of weak structural balance in signed networks naturally leads to a global low-rank model for the network. Under such a model, the sign inference problem can be formulated as a low-rank matrix completion problem. We show that we can perfectly recover missing relationships, under certain conditions, using state-of-the-art matrix completion algorithms. We also propose the use of a low-rank matrix factorization approach with generalized loss functions as a practical method for sign inference - this approach yields high accuracy while being scalable to large signed networks, for instance, we show that this analysis can be performed on a synthetic graph with 1.1 million nodes and 120 million edges in 10 minutes. We further show that the low-rank model can be used for other analysis tasks on signed networks, such as user segmentation through signed graph clustering, with theoretical guarantees. Experiments on synthetic as well as real data show that our low rank model substantially improves accuracy of sign inference as well as clustering. As an example, on the largest real dataset available to us (Epinions data with 130K nodes and 840K edges), our matrix factorization approach yields 94.6 accuracy on the sign inference task as compared to 90.8 accuracy using a state-of-the-art cycle-based method - moreover, our method runs in 40 seconds as compared to 10,000 seconds for the cycle-based method. Users in online social networks play a variety of social roles and statuses. For example, users in Twitter can be represented as advertiser, content contributor, information receiver, etc; users in Linkedin can be in different professional roles, such as engineer, salesperson and recruiter. Previous research work mainly focuses on using categorical and textual information to predict the attributes of users. However, it cannot be applied to a large number of users in real social networks, since much of such information is missing, outdated and non-standard. In this paper, we investigate the social roles and statuses that people act in online social networks in the perspective of network structures, since the uniqueness of social networks is connecting people. We quantitatively analyze a number of key social principles and theories that correlate with social roles and statuses. We systematically study how the network characteristics reflect the social situations of users in an online society. We discover patterns of homophily, the tendency of users to connect with users with similar social roles and statuses. In addition, we observe that different factors in social theories influence the social role status of an individual user to various extent, since these social principles represent different aspects of the network. We then introduce an optimization framework based on Factor Conditioning Symmetry, and we propose a probabilistic model to integrate the optimization framework on local structural information as well as network influence to infer the unknown social roles and statuses of online users. We will present experiment results to show the effectiveness of the inference. The emergence of very large hierarchies that result from the increase in available data raises many problems of visualization and navigation. On data sets of such scale, classical graph drawing methods do not take advantage of certain human cognitive skills such as shape recognition. These cognitive skills could make it easier to remember the global structure of the data. In this paper, we propose a method that is based on the use of nested irregular shapes. We name it GosperMap as we rely on the use of a Gosper Curve to generate these shapes. By employing human perception mechanisms that were developed by handling, for example, cartographic maps, this technique facilitates the visualization and navigation of a hierarchy. An algorithm has been designed to preserve region containment according to the hierarchy and to set the leaves' sizes proportionally to a property, in such a way that the size of nonleaf regions corresponds to the sum of their children's sizes. Moreover, the input ordering of the hierarchy's nodes is preserved, i.e., the areas that represent two consecutive children of a node in the hierarchy are adjacent to one another. This property is especially useful because it guarantees some stability in our algorithm. We illustrate our technique by providing visualization examples of the repartition of tax money in the US over time. Furthermore, we validate the use of the GosperMap in a professional documentation context and show the stability and ease of memorization for this type of map. Detection of community structures in social networks has attracted lots of attention in the domain of sociology and behavioral sciences. Social networks also exhibit dynamic nature as these networks change continuously with the passage of time. Social networks might also present a hierarchical structure led by individuals who play important roles in a society such as managers and decision makers. Detection and visualization of these networks that are changing over time is a challenging problem where communities change as a function of events taking place in the society and the role people play in it. In this paper, we address these issues by presenting a system to analyze dynamic social networks. The proposed system is based on dynamic graph discretization and graph clustering. The system allows detection of major structural changes taking place in social communities over time and reveals hierarchies by identifying influential people in social networks. We use two different data sets for the empirical evaluation and observe that our system helps to discover interesting facts about the social and hierarchical structures present in these social networks.