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A FLEXIBLE PARAMETERIZATION FOR BASELINE MEAN DEGREE IN MULTIPLE-NETWORK ERGMS.

Carter T Butts1, Zack W Almquist2

  • 1Departments of Sociology, Statistics, and EECS, and Institute for Mathematical Behavioral Sciences, University of California, Irvine, California, USA.

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|September 15, 2015
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Summary
This summary is machine-generated.

We introduce a new parameterization for exponential family random graph models (ERGM) to better model networks of varying sizes. This flexible approach allows baseline expected degree to scale with network order, improving graph analysis.

Keywords:
baseline modelsexponential family random graph models (ERGMs)mean degreemodel parameterization

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Area of Science:

  • Network analysis
  • Statistical modeling
  • Computational social science

Background:

  • Conventional exponential family random graph models (ERGM) have a baseline density constant in graph order.
  • This can be problematic for modeling multiple networks with different numbers of nodes.
  • Previous work proposed an ERGM alternative yielding constant expected mean degree.

Purpose of the Study:

  • To propose an alternative ERGM parameterization for flexible modeling of networks.
  • To enable baseline expected degree to scale as an arbitrary power of graph order.
  • To provide a method for analyzing networks of varying sizes and structures.

Main Methods:

  • Extended an existing alternative ERGM parameterization.
  • Introduced a new parameterization incorporating an edge count and log order statistic.
  • Utilized traditional edge count statistic alongside the new statistic in model specification.

Main Results:

  • The proposed parameterization allows for flexible modeling of baseline expected degree scaling with network order.
  • This method is easily implemented within ERGM frameworks.
  • Facilitates more accurate analysis of networks with heterogeneous orders.

Conclusions:

  • The novel ERGM parameterization offers enhanced flexibility for network analysis.
  • It addresses limitations of conventional models when dealing with varying graph orders.
  • This approach improves the ability to model and understand complex network structures.