As we rapidly continue into the information age, the rate at which data is produced has created an unprecedented demand for novel methods to effectively extract insightful patterns. We can then seek to understand the past, make predictions about the future, and ultimately take actionable steps towards improving our society. Thus, due to the fact that much of today's big data can be represented as graphs, emphasis is being taken to harness the natural structure of data through network analysis. Traditionally, network analysis has focused on networks having only positive links, or unsigned networks. However, in many real-world systems, relations between nodes in a graph can be both positive and negative, or signed networks. For example, in online social media, users not only have positive links such as friends, followers, and those they trust, but also can establish negative links to those they distrust, towards their foes, or block and unfriend users.Thus, although signed networks are ubiquitous due to their ability to represent negative links in addition to positive links, they have been significantly under explored. In addition, due to the rise in popularity of today's social media and increased polarization online, this has led to both an increased attention and demand for advanced methods to perform the typical network analysis tasks when also taking into consideration negative links. More specifically, there is a need for methods that can measure, model, mine, and apply signed networks that harness both these positive and negative relations. However, this raises novel challenges, as the properties and principles of negative links are not necessarily the same as positive links, and furthermore the social theories that have been used in unsigned networks might not apply with the inclusion of negative links.The chief objective of this dissertation is to first analyze the distinct properties negative links have as compared to positive links and towards improving network analysis with negative links by researching the utility and how to harness social theories that have been established in a holistic view of networks containing both positive and negative links. We discover that simply extending unsigned network analysis is typically not sufficient and that although the existence of negative links introduces numerous challenges, they also provide unprecedented opportunities for advancing the frontier of the network analysis domain. In particular, we develop advanced methods in signed networks for measuring node relevance and centrality (i.e., signed network measuring), present the first generative signed network model and extend/analyze balance theory to signed bipartite networks (i.e., signed network modeling), construct the first signed graph convolutional network which learns node representations that can achieve state-of-the-art prediction performance and then furthermore introduce the novel idea of transformation-based network embedding (i.e., signed network mining), and apply signed networks by creating a framework that can infer both link and interaction polarity levels in online social media and constructing an advanced comprehensive congressional vote prediction framework built around harnessing signed networks.
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