α-Indirect Control in Onion-like Networks

We propose a fast, accurate, and scalable algorithm to detect ultimate controlling entities in global corporate networks. α-ICON uses company-participant links to identify super-holders who exert control in networks with millions of nodes.

By exploiting onion-like properties of such networks we iteratively peel off the hanging vertices until a dense core remains. This procedure allows for a dramatic speed-up, uncovers meaningful structures, and handles circular ownership by design.

Read our paper with the applications. As a toy example, consider the below corporate network where α-ICON designates Mr Philip Mactaggart (in green) as the super-holder exerting control over all other entities, directly or indirectly held:

Installation

To replicate the analysis you need to clone this repository to your local machine. Then you need to install the required versions of R dependencies listed in DEPENDENCIES. code/helper_functions/install_dependencies.r automates this step, but you may still need to install the underlying libraries manually with Homebrew or apt-get, depending on your platform. Finally, you need to declare the environment variable ALPHAICON_PATH in bash pointing to the repository. Or, better yet, you can add it in your .Renviron with

> ~/.Renviron “>

user:~$ echo 'ALPHAICON_PATH="path_to_cloned_repository"' >> ~/.Renviron

The repository does not contain any data due to its size (10+ GB unpacked); most files in data/ and output/ folders are zero-byte placeholders. We provide a public Google Drive folder with the populated data/ and output/ directories. You may still need to unzip them manually.

A self-contained example of α-ICON is also available in Google Colaboratory.

Repository structure

data/
├─uk/ # Data on UK companies and participants
| ├ persons-with-significant-control-snapshot-2021-08-02.txt # Source PSC data
| ├ BasicCompanyDataAsOneFile-2021-08-01.csv # Source data on live companies in UK
| ├ sic_2007_code_list.csv # Standard Industrial Classification codes
| ├ psc_snapshot_2021-08-02.rdata # Processed People with Significant Control data
| └ uk_basic_companies_data_2021-08-01.rdata # Processed Basic Company data
|
├─corpwatch_api_tables_csv_14aug21/ # Data from CorpWatch Dump 
| ├ company_info.csv # Source companies data from SEC filings
| ├ cik_name_lookup.csv # Company name variants in SEC filings
| └ company_locations.csv # Company locations in SEC filings
|
code/
├─helper_functions/
| ├ install_dependencies.r # Installs R dependencies used in the project 
| └ compute_power_index.r # Computes Mizuno et al. (2020) DPI and NPI
|
├─data_preparation/
| └─uk/
|   ├ 1a_process_psc_snapshot.r # Prepare source PSC data
|   ├ 1b_process_companies_data.r # Prepare source data on live companies
|   ├ 2_psc_snapshot_to_participants_panel.r # PSC data to entity-participant info
|   └ 3_prepare_affiliated_entities_evaluation_data.r # Process CorpWatch data
|
├─alphaicon_paper/
| ├ 1_compute_alphaicon.ipynb # Jupyter Notebook w. α-ICON (also on Google Colab)
| ├ 2_compute_npi_dpi.r # Computation of Direct and Network Power Indices
| ├ 3_summary_stat_by_node_type.r # UK PSC network statistics by core/SH/ST/I
| ├ 4_illustrate_algorithm.r # Visualise selected networks
| ├ 5_algorithm_evaluation.r # Compute recall @ k and l for various algorithms
| └ 6_rank_top_holders.r # Examine the rankings of super-holders & Kendall's tau
|
output/
├─uk/
| ├ uk_organisations_participants_2021_long_2aug21.csv # Primary ownership data
| ├ uk_organisations_participation_graph_core_periphery_membership_6aug21.csv
| ├─npi_dpi/ # Mizuno et al. (2020) computation results on UK PSC data
| | └─10000iter/
| |   ├ uk_organisations_participants_2021_long_7sep21_dpi_10000iter.csv # DPI
| |   └ uk_organisations_participants_2021_long_7sep21_npi_10000iter.csv # NPI
| |
| ├─transitive/ # Computed α-ICON shares on equity shares or DPI weights
| | ├ uk_organisations_transitive_ownership_alpha*_2021_long_2aug21.csv # α = *
| | └ uk_organisations_transitive_ownership_alpha*_2021_long_7sep21_dpi_....csv
| |
└─alphaicon_paper/
  ├ uk_orgs_algorithm_evaluation_recall.csv # Algorithm recall by k
  ├ uk_orgs_algorithm_evaluation_recall_by_pathlength.csv # Algorithm recall by l
  ├ uk_organisations_top100_holders_2021_long_2aug21.csv # Top SH in PSC network
  ├ uk_organisations_top100_holders_diff_npi_dpi_2021_long_2aug21.csv # Top-100 SH
  |                          # with the largest difference betw. total DPI and NPI
  ├ uk_organisations_top100_holders_diff_transitive_dpi_2021_long_2aug21.csv
  |  # Top-100 SH with the largest difference betw. total DPI and α-ICON (α=0.999)
  ├ uk_organisations_top100_holders_diff_transitive_npi_2021_long_2aug21.csv
  |  # Top-100 SH with the largest difference betw. total NPI and α-ICON (α=0.999)
  └ network_examples/ # Visualisations of selected networks

We provide an annotated Makefile that documents the data analysis in our papers.

To build the ‘α-Indirect Control in Onion-like Networks’ paper run make alphaicon_paper when in the repository folder.

Please note that those commands will not produce any publication-ready output files (e.g. tables or figures): the export statements are commented out in the code. Our intention is to make the analysis pipeline transparent to the readers with the aid of make: