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Network Representations of Complex Systems

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Book cover Network Analysis Literacy

Part of the book series: Lecture Notes in Social Networks ((LNSN))

Abstract

Network analysis starts with the available data on relationships between entities of the complex system to observe. In this chapter, the main modeling decisions to turn a raw data set into a complex network are discussed.

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Notes

  1. 1.

    Of course, Plato would not have referred to the “real” complex system but to the ideal complex network, where the word ideal refers to the pure concept of the thing of interest.

  2. 2.

    Another very important aspect of this is that it is in general difficult to give information about entities without disclosing their identity. This has hindered many publications of interesting data sets.

  3. 3.

    Whatever your favorite definition of “social network” is at the moment.

  4. 4.

    An API is an Application Programming Interface, a set of functions which allows programmers to get access to information.

  5. 5.

    There is hope, however. Kergl et al. made a clever analysis of the timestamps of Twitter messages from the sample and they convincingly show that it is very likely the case that Twitter sends out a uniform 10 \(\%\) sample [17].

  6. 6.

    The statistical significance of co-occurrence is discussed in more detail in Sect. 13.5.

  7. 7.

    A partition divides a set S into subsets such that each element of S is in exactly one of the subsets, s. Sect. 3.3.2.

  8. 8.

    In general, the Jaccard-coefficient of two sets S and T is defined as the number of common elements divided by the number of elements that occur in at least one of the two sets. This is written as: \(Jacc(S,T)=\frac{|S\cap T|}{|S\cup T}\).

  9. 9.

    The projection onto the right-hand side nodes is analogous, based on a similarity function \(\sigma : R\times R \rightarrow \mathbb R\).

  10. 10.

    Kahnemann and Vernon L. Smith were awarded the Noble prize in 2002 for their work with Tversky, who was already deceased at that time point. Noble prizes are not awarded post-mortem.

  11. 11.

    The notation \(\left( {\begin{array}{c}k\\ 2\end{array}}\right) \) denotes the number of different subsets of size 2 out of k different objects.

  12. 12.

    There are way more of these than a non-biologists might think! It is a classic instance of an “entity resolution” problem.

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Authors and Affiliations

  1. TU Kaiserslautern, FB Computer Science, Graph Theory and Analysis of Complex Networks, Gottlieb-Daimler-Str. 48, 67331, Kaiserslautern, Germany

    Katharina A. Zweig

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  1. Katharina A. Zweig
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Correspondence to Katharina A. Zweig .

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Zweig, K.A. (2016). Network Representations of Complex Systems. In: Network Analysis Literacy. Lecture Notes in Social Networks. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0741-6_5

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  • DOI: https://doi.org/10.1007/978-3-7091-0741-6_5

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