Abstract
Topological measures are crucial to describe, classify and understand complex networks. Lots of measures are proposed to characterize specific features of specific networks, but the relationships among these measures remain unclear. Taking into account that pulling networks from different domains together for statistical analysis might provide incorrect conclusions, we conduct our investigation with data observed from the same network in the form of simultaneously measured time series. We synthesize a transfer entropy-based framework to quantify the relationships among topological measures, and then to provide a holistic scenario of these measures by inferring a drive-response network. Techniques from Symbolic Transfer Entropy, Effective Transfer Entropy, and Partial Transfer Entropy are synthesized to deal with challenges such as time series being non-stationary, finite sample effects and indirect effects. We resort to kernel density estimation to assess significance of the results based on surrogate data. The framework is applied to study 20 measures across 2779 records in the Technology Exchange Network, and the results are consistent with some existing knowledge. With the drive-response network, we evaluate the influence of each measure by calculating its strength, and cluster them into three classes, i.e., driving measures, responding measures and standalone measures, according to the network communities.
Highlights
We will quantify the relationships between measures based on these time series with transfer entropy, and construct a drive-response network which stands for the relation pattern among these topological measures, as shown in the lower half of Figure 1
Taking into account that pulling networks from different domains and topologies together for statistical analysis might provide incorrect conclusions [25], we conduct our investigation with the data observed from the same network in the form of simultaneously measured time series
In order to reveal the relationships among topological measures from their time series, we synthesize a practical framework comprising techniques from Symbolic Transfer Entropy, Effective Transfer Entropy, and Partial Transfer Entropy, which is able to deal with the challenges such as time series being nonstationary, time series being continuous, finite sample effects and indirect effects
Summary
The last decade has witnessed a flourishing progress of network science in many interdisciplinary fields [1,2,3]. It is proved both theoretical and practically that topological measures are essential to complex network investigations, including representation, characterization, classification and modeling [4,5,6,7,8]. Each measure alone is of practical importance and can capture some meaningful properties of the network under study, but when so many measures are put together we will find that they are obviously not “Mutually Exclusive and Collectively Exhaustive”, namely, some measures fully or partly capture the same information provided by others while there are still properties that cannot be captured by any of the existing measures. With the increasing popularity of network analyses, the question which topological measures offer complementary or redundant information has become more important [13]
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