Barabási (2016) Network Science.
Citation: Barabási, Albert-László (2016) Network Science, retrieved from http://networksciencebook.com.
Summary The book is concerned with assessing the role of networks in various social phenomenon, and providing a methodology for doing so — including the articulation of their own model (Barabási-Albert). Chapter one examines the vulnerabilities emerging from networks, the links between these vulnerabilities and complex (interconnected systems), and the scholarly evolution of the study of networks and its impact.
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Concepts and Definitions: Barabási (2016): community: “a group of nodes that have a higher likelihood of connecting to each other than to nodes from other communities.” A random network is not expected to have communities, because the connection pattern between nodes is expected to be uniform.
Barabási (2016): Defining Communities: Cliques: “A clique corresponds to a complete subgraph.” Triangles are frequent in networks, but larger cliques are rare. Strong Communities: “a connected subgraph whose nodes have more links to other nodes in the same community that to nodes that belong to other communities.” Weak Communities: “a subgraph whose nodes’ total internal degree exceeds their total external degree.”
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Argument/Conclusion: Barabási (2016): Understanding the structure of networks helps us avoid or mitigate the vulnerabilities that may be caused by the complexity of systems, and at the same time amplify the positive benefits that such complexity can bring. “we will never understand complex systems unless we develop a deep understanding of the networks behind them.” To achieve this understanding, we must be able to rigorously assess them. And we need to understand how changes to the network affect its overall stability.
Presumptions: Network behaviours follow set rules that can be mapped, and therefore network behaviours can be predicted (notably, many of the examples used in the introduction are either of technical systems or from natural sciences). Whatever their domain, networks are “governed by the same organizing principles,” which can therefore be explored mathematically. Vulnerability is a key concern in understanding networks. System complexity is a distinguishing feature of the modern world. Network science is interdisciplinary, empirical and data driven, and quantitative, mathematical and computational in nature. Its significance stems in part from the fact that it has an impact beyond the boundaries of a single discipline, and it is only possible to map networks because of advances in computational science. Social networks are “the fabric of the society and determines the spread of knowledge, behavior and resources.” One needs to understand the mathematical models in order to properly apply network analysis.
Limitations/Flaws: [The concept of intellectual worlds is based on a fundamentally different epistemological basis to the theory of ‘network science’ articulated by Barabasi. This science is inherently postivist in its understanding of the world. Yet one does not need to be positivist to accept that networks can tell us something useful about the world]
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Notes: Barabási (2016): Random networks are those where the likelihood of links between any nodes are within an equal probability range. This explicitly rules out the possibility of hubs forming. In reality, there are no truly random networks, and networks are scale-free because they don’t have fixed rules for probability ranges. Instead, they follow a power distribution law that states that hubs will emerge, e.g. around powerful or wealthy individuals. The distance between two hubs is usually shorter than the distance between two ‘normal’ nodes because of the number of connections they have, and therefore they represent the shortest paths between any two nodes. The random network model overestimates the distance between any two nodes by missing out the hubs.
Barabási (2016): “to understand the properties of real networks, it is often sufficient to remember that in scale-free networks a few highly connected hubs coexist with a large number of small nodes.”