marcessz/complex-networks

Supplementary data for the paper titled Network classification-based structural analysis of real networks and their model-generated counterparts.

Network classification-based structural analysis of real networks and their model-generated counterparts

Supplementary data for the paper: Nagy, M., & Molontay, R. (2022). Network classification-based structural analysis of real networks and their model-generated counterparts. Network Science, 1-24.

How to Cite

@article{nagy2022network,
  title={Network classification-based structural analysis of real networks and their model-generated counterparts},
  author={Nagy, Marcell and Molontay, Roland},
  journal={Network Science},
  pages={1--24},
  year={2022},
  publisher={Cambridge University Press}
}

Source

The graphs are collected from the following sources:

• Network Repository,
• The Colorado Index of Complex Networks (ICON),
• NeuroData's Graph DataBase,
• KONECT - The Koblenz Network Collection,
• Interaction Web Database (IWDB),
• Transportation Networks for Research,
• Centre for Water Systems

The collected networks canbe found in the networks folder

Summary of Networks

Domain	Description	Range of network size	Number of networks
Brain	Human and animal connectomes	50-2,995 (avg: 946)	100
Cheminformatics	Protein-protein (enzyme) interaction networks	44-125 (avg: 55)	100
Food	What-eats-what, consumer-resource networks	19-1,500 (avg: 118)	100
Infrastructural	Transportation (metro, bus, road, airline) and distribution networks (power and water)	39-40K (avg: 4,562)	68
Social	Facebook, Twitter and collaboration networks	85-34K (avg: 5,183)	118
Web	Pieces of the World Wide Web	146-16K (avg: 4,488)	14

Graph Measurements

The data folder contains a spreadsheet that contains the calculated metrics of the 482 real networks.

The calculated metrics are the following:

• assortativity,
• average clustering coefficient,
• average degree,
• average path length,
• density,
• global clustering coefficient,
• four interval degree probabilities introduced in this paper,
• largest eigenvector centrality,
• maximum degree,
• maximum edge betweenness centrality,
• maximum vertex betweenness centrality,
• number of edges,
• number of nodes,
• pseudo diameter

A detailed description of the dataset and the metrics can be found in Network classification-based structural analysis of real networks and their model-generated counterparts and in Data-driven Analysis of Complex Networks and their Model-generated Counterparts

Supplementary material

Analysis of network models

According to the Random Forest classifier, when the goal is to predict whether the network is real or model-generated, the most distinguishing graph metrics are the normalized average path length, the average clustering coefficient, the maximum eigenvector centrality, and the assortativity.

The following figures show the structural properties of the real networks that the network models cannot capture. In other words, the distribution of the most distinguishing graph metrics of the real networks and the model-generated graphs.

Stability of the networks

Since the network models generate random graphs, the question naturally comes up: How robust are the graph metrics of the fitted models with fixed parameters? We have analyzed the sensitivity of the models on six different-sized graphs from different domains, the chosen networks are detailed in the table below. For each of these six real networks, we fitted each network model and then generated 30 graph instances with each model using the previously fitted parameter settings. For the sensitivity analysis, we studied the distribution of the graph measurements of the graph instances.

Domain	Name	Size	Number of edges
Social	ca-AstroPh (Leskovec et al., 2007)	17,903	196,972
Web	Darkweb (Griffith et al., 2017)	7,178	24,879
Brain	Jung2015 (Kiar, 2016)	2,989	31,548
Infrastructure	ABN (Chatterjee et al., 2016)	1,103	2,150
Food	Srep (Dunne et al., 2016)	235	1,743
Cheminformatics	Enzymes-g292 (Canning et al., 2018)	60	100

Social network (ca-AstroPh)

Web network (Darkweb)

Brain network (Jung2015)

Infrastructure network (ABN)

Food network (Srep)

Cheminformatics network (Enzymes-g292)