Narrative structure ofA Song of Ice and Firecreates a fictional world with realistic measures of social complexity

Network science and data analytics are used to quantify static and dynamic structures in George R. R. Martin’s epic novels,A Song of Ice and Fire, works noted for their scale and complexity. By tracking the network of character interactions as the story unfolds, it is found that structural properties remain approximately stable and comparable to real-world social networks. Furthermore, the degrees of the most connected characters reflect a cognitive limit on the number of concurrent social connections that humans tend to maintain. We also analyze the distribution of time intervals between significant deaths measured with respect to the in-story timeline. These are consistent with power-law distributions commonly found in interevent times for a range of nonviolent human activities in the real world. We propose that structural features in the narrative that are reflected in our actual social world help readers to follow and to relate to the story, despite its sprawling extent. It is also found that the distribution of intervals between significant deaths in chapters is different to that for the in-story timeline; it is geometric rather than power law. Geometric distributions are memoryless in that the time since the last death does not inform as to the time to the next. This provides measurable support for the widely held view that significant deaths inA Song of Ice and Fireare unpredictable chapter by chapter.

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Revisiting Power-law Distributions in Spectra of Real World Networks

Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '17 ◽

10.1145/3097983.3098128 ◽

2017 ◽

Cited By ~ 6

Author(s):

Nicole Eikmeier ◽

David F. Gleich

Keyword(s):

Power Law ◽

Real World ◽

Power Law Distributions

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Classes of preferential attachment and triangle preferential attachment models with power-law spectra

Journal of Complex Networks ◽

10.1093/comnet/cnz040 ◽

2019 ◽

Vol 8 (4) ◽

Cited By ~ 1

Author(s):

Nicole Eikmeier ◽

David F Gleich

Keyword(s):

Power Law ◽

Real World ◽

Preferential Attachment ◽

Power Laws ◽

Network Data ◽

Degree Sequences ◽

Graph Models ◽

Attachment Model ◽

Power Law Distributions ◽

Real Network Data

Abstract Preferential attachment (PA) models are a common class of graph models which have been used to explain why power-law distributions appear in the degree sequences of real network data. Among other properties of real-world networks, they commonly have non-trivial clustering coefficients due to an abundance of triangles as well as power laws in the eigenvalue spectra. Although there are triangle PA models and eigenvalue power laws in specific PA constructions, there are no results that existing constructions have both. In this article, we present a specific Triangle Generalized Preferential Attachment Model that, by construction, has non-trivial clustering. We further prove that this model has a power law in both the degree distribution and eigenvalue spectra.

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Recognizing Power-law Graphs by Machine Learning Algorithms using a Reduced Set of Structural Features

10.5753/eniac.2019.9319 ◽

2019 ◽

Cited By ~ 1

Author(s):

Alane Lima ◽

André Vignatti ◽

Murilo Silva

Keyword(s):

Machine Learning ◽

Power Law ◽

Real World ◽

Optimization Problems ◽

Learning Algorithms ◽

Structural Features ◽

Machine Learning Algorithms ◽

Graph Representation ◽

Gradient Boosting ◽

Graph Properties

The empirical study of large real world networks in the last 20 years showed that a variety of real-world graphs are power-law. There are evidence that optimization problems seem easier in these graphs; however, for a given graph, classifying it as power-law is a problem in itself. In this work, we propose using machine learning algorithms (KNN, SVM, Gradient Boosting and Random Forests) for this task. We suggest a graph representation based on [Canning et al. 2018], but using a much simplified set of structural properties of the graph. We compare the proposed representation with the one generated by the graph2vec framework. The experiments attained high accuracy, indicating that a reduced set of structural graph properties is enough for the presented problem.

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The structure of real-world networks

10.1093/oso/9780198805090.003.0010 ◽

2018 ◽

Author(s):

Mark Newman

Keyword(s):

Power Law ◽

Real World ◽

Small World ◽

Component Structure ◽

Scale Free ◽

Scale Free Networks ◽

Path Lengths ◽

Power Law Distributions

This chapter brings together the ideas and techniques developed in previous chapters, applying them to a range of real-world networks to describe and understand the structure of those networks. Topics discussed include the observed component structure of networks, average path lengths between nodes and the small-world effect, degree distributions including power-law distributions and scale-free networks, clustering and transitivity, and assortative mixing.

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Sublinear domination and core–periphery networks

Scientific Reports ◽

10.1038/s41598-021-94105-8 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Marios Papachristou

Keyword(s):

Network Model ◽

Power Law ◽

Real World ◽

Random Network ◽

Small World ◽

The Core ◽

Entire Network

AbstractIn this paper we devise a generative random network model with core–periphery properties whose core nodes act as sublinear dominators, that is, if the network has n nodes, the core has size o(n) and dominates the entire network. We show that instances generated by this model exhibit power law degree distributions, and incorporates small-world phenomena. We also fit our model in a variety of real-world networks.

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Maximal modularity and the optimal size of parliaments

Scientific Reports ◽

10.1038/s41598-021-93639-1 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Luca Gamberi ◽

Yanik-Pascal Förster ◽

Evan Tzanis ◽

Alessia Annibale ◽

Pierpaolo Vivo

Keyword(s):

Power Law ◽

Real World ◽

Empirical Data ◽

Random Network ◽

Functional Relation ◽

Optimal Size ◽

Real World Data ◽

Universal Power Law ◽

The Empirical Analysis ◽

Democratic Country

AbstractAn important question in representative democracies is how to determine the optimal parliament size of a given country. According to an old conjecture, known as the cubic root law, there is a fairly universal power-law relation, with an exponent equal to 1/3, between the size of an elected parliament and the country’s population. Empirical data in modern European countries support such universality but are consistent with a larger exponent. In this work, we analyse this intriguing regularity using tools from complex networks theory. We model the population of a democratic country as a random network, drawn from a growth model, where each node is assigned a constituency membership sampled from an available set of size D. We calculate analytically the modularity of the population and find that its functional relation with the number of constituencies is strongly non-monotonic, exhibiting a maximum that depends on the population size. The criterion of maximal modularity allows us to predict that the number of representatives should scale as a power-law in the size of the population, a finding that is qualitatively confirmed by the empirical analysis of real-world data.

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