Mark-Kramer / MultilayerBenchmark

A generative model for mesoscale structure in multilayer networks implemented in MATLAB

MultilayerBenchmark Version 1.0

released November 2016

Please cite this code as Lucas G. S. Jeub and Marya Bazzi "A generative model for mesoscale structure in multilayer networks implemented in MATLAB," https://github.com/MultilayerBenchmark/MultilayerBenchmark (2016)

This package consists of code for the generative model in [1]. It allows a user to generate multilayer networks with planted mesoscale structure (e.g., community structure) in a principled and customisable way.

Our code consists of a main DirichletDCSBMBenchmark.m file which contains two main subroutines:

1. PartitionGenerator.m which constructs a planted multilayer partition, and
2. DCSBMNetworkGenerator.m which constructs a multilayer network for a given planted multilayer partition.

To use this code, the minimal input that needs to be specified by a user is:

• number of nodes in each layer
• number of layers, and
• an interlayer dependency tensor that specifies the desired dependency structure between layers (note that the order of the layers, whenever present, needs to be respected in the interlayer dependency tensor). We include three useful examples of interlayer dependency tensors in TemporalDependencyMatrix.m, MultiplexDependencyMatrix.m, and BlockMultiplexDependencyMatrix.m

The subroutines (1) and (2) have various parameters (which we set to a default parameter choice) that a user can modify as needed. For example, one can:

• vary the number of nodes in each layer
• vary the minimum and maximum expected degrees in each layer
• vary the mixing parameter in the planted partition network model
• vary the expected number of communities in the multilayer partition
• control which community labels are present or absent in each layer
• include ordered (e.g., time) and unordered aspects (e.g., social media platforms) in the same multilayer partition
• vary the parameters of the Dirichlet null distribution to alter expected community sizes in the multilayer partition
• use a "null distribution" other than the Dirichlet null distribution in PartitionGenerator.m

Furthermore, a user can use any monolayer network model with a planted partition other than DCSBM by using a function other than DCSBMNetworkGenerator.m to generated edges for a given planted partition.

Importantly, the subroutines (1) and (2) are carried out successively in our code and not in parallel, and each can be modified independently as needed.

Note that Version 1.0 of the code only generates (interdependent) intralayer edges for a given multilayer partition. One can modify it to generate interlayer and/or intralayer edges (see Section 4 in [1]).

More extensive documentation is provided in each function and example use of this code is provided in examples_script.m. See also [1] for a detailed explanation of our generative model (see in particular Section 3 "Generating Sampled Multilayer Partitions" and Section 4 "Sampling Network Edges").

##References:

[1] Generative benchmark models for mesoscale structure in multilayer networks, M. Bazzi, L. G. S. Jeub, A. Arenas, S. D. Howison, M. A. Porter. arXiv:1608.06196.

##Acknowledgments:

A special thank you to Sam D. Howison, Mason A. Porter, and Alex Arenas for contributing ideas that have helped develop our generative model for mesoscale structure in multilayer networks.