Abstract
Tremendous advances have been made in our understanding of the properties and evolution of complex networks. These advances were initially driven by information-poor empirical networks and theoretical analysis of unweighted and undirected graphs. Recently, information-rich empirical data complex networks supported the development of more sophisticated models that include edge directionality and weight properties, and multiple layers. Many studies still focus on unweighted undirected description of networks, prompting an essential question: how to identify when a model is simpler than it must be? Here, we argue that the presence of centrality anomalies in complex networks is a result of model over-simplification. Specifically, we investigate the well-known anomaly in betweenness centrality for transportation networks, according to which highly connected nodes are not necessarily the most central. Using a broad class of network models with weights and spatial constraints and four large data sets of transportation networks, we show that the unweighted projection of the structure of these networks can exhibit a significant fraction of anomalous nodes compared to a random null model. However, the weighted projection of these networks, compared with an appropriated null model, significantly reduces the fraction of anomalies observed, suggesting that centrality anomalies are a symptom of model over-simplification. Because lack of information-rich data is a common challenge when dealing with complex networks and can cause anomalies that misestimate the role of nodes in the system, we argue that sufficiently sophisticated models be used when anomalies are detected.
Highlights
The study of complex networks produced fruitful results in many areas of knowledge, from systems biology [1, 2] and social systems [3, 4] to epidemiology [5,6,7] and statistical physics [8, 9]
Using a broad class of network models with weights and spatial constraints and four large data sets of transportation networks, we show that the unweighted projection of the structure of these networks can exhibit a significant fraction of anomalous nodes compared to a random null model
Because lack of informationrich data is a common challenge when dealing with complex networks and can cause anomalies that misestimate the role of nodes in the system, we argue that sufficiently sophisticated models be used when anomalies are detected
Summary
The study of complex networks produced fruitful results in many areas of knowledge, from systems biology [1, 2] and social systems [3, 4] to epidemiology [5,6,7] and statistical physics [8, 9]. The initial focus of complex networks and graph theory was on undirected, unweighted topologies [9, 10]. Many properties were proved to be effective in describing complex systems [11,12,13,14]. Weighted, directed, multiplexed networks have been the focus of much research attention. In many cases, these more sophisticated representations of the system are most appropriate to describe real-world networks [15,16,17,18]. Researchers still fall back on representing a system’s network of interactions as if it was undirected and unweighted, many times because of the lack of information-rich data sets
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