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2 results

  • Chapter 12 - Understanding network structure and organization

  • from Part II - Applications, tools, and tasks
  • James Bagrow, University of Vermont, Yong‐Yeol Ahn, Indiana University, Bloomington
  • Book:
    Working with Network Data
    Published online:
    06 June 2024
    Print publication:
    13 June 2024, pp 165-202

  • Summary

    In this chapter, we focus on statistics and measures that quantify a networks structure and characterize how it is organized. These measures have been central to much of network science, and a vast array of material is available to us, spanning across all scales of the network. The measures we discuss include general-purpose measures and those specialized to particular circumstances, which allow us to better get a handle on the network data. Network science has generated a dizzying array of valuable measures over the years. For example, we can measure local structures, motifs, patterns of correlations within the network, clusters and communities, hierarchy, and more. These measures are used for exploratory and confirmatory analyses, which we discussed in the previous chapter. With the measures of this chapter, we can understand the patterns in our networks, and using statistical models, we can put those patterns on a firm foundation.

  • Degree correlations in scale-free random graph models

  • Part of
  • Clara Stegehuis
  • Journal:
    Journal of Applied Probability / Volume 56 / Issue 3 / September 2019
    Published online by Cambridge University Press:
    01 October 2019, pp. 672-700
    Print publication:
    September 2019

  • We study the average nearest-neighbour degree a(k) of vertices with degree k. In many real-world networks with power-law degree distribution, a(k) falls off with k, a property ascribed to the constraint that any two vertices are connected by at most one edge. We show that a(k) indeed decays with k in three simple random graph models with power-law degrees: the erased configuration model, the rank-1 inhomogeneous random graph, and the hyperbolic random graph. We find that in the large-network limit for all three null models, a(k) starts to decay beyond $n^{(\tau-2)/(\tau-1)}$ and then settles on a power law $a(k)\sim k^{\tau-3}$, with $\tau$ the degree exponent.