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Fast Generation of Sparse Random Kernel Graphs.

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Summary
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We introduce random kernel graphs, a flexible model for complex networks. Our efficient algorithm generates large sparse graphs with tunable properties in near-linear time.

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Area of Science:

  • Network Science
  • Graph Theory
  • Computational Mathematics

Background:

  • Kernel-based inhomogeneous random graphs offer flexibility and mathematical tractability for modeling real-world networks.
  • Existing models often struggle with scalability for large networks.

Purpose of the Study:

  • To introduce a novel class of inhomogeneous random graph models called random kernel graphs.
  • To develop an efficient algorithm for generating sparse random kernel graphs with tunable properties.
  • To demonstrate the algorithm's scalability for large networks.

Main Methods:

  • Specification of the random kernel graph model.
  • Development of an efficient graph generation algorithm.
  • Analysis of algorithm runtime complexity.
  • Application to generating power-law degree distribution graphs with tunable assortativity.

Main Results:

  • The proposed random kernel graph model produces sparse graphs with controllable properties.
  • The generation algorithm achieves a runtime complexity of at most O(n(logn)^2) for many practical kernels.
  • The algorithm efficiently generates samples of power-law degree distribution graphs with tunable assortativity.

Conclusions:

  • Random kernel graphs provide a powerful and efficient framework for modeling complex networks.
  • The developed algorithm offers a scalable solution for generating large, realistic network instances.
  • This approach facilitates the study of network properties like degree distribution and assortativity.