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Computing Inter-City Matrix and Global Network Connectivities with R - A Brief Guide

T. Storme and B. Derudder^*

Introduction

This document contains R code that can be used to transform two-mode service value matrices (svm) into one-mode inter-city connectivity matrices (icc) using the interlocking network model (inm) , and subsequently compute the global network connectivity (gnc) for every city. Details on the input matrices, the model, and its output can be found in .

is a free software environment that provides a wide variety of statistical techniques. R needs to be downloaded, together with a development environment that supports direct code execution, and tools for plotting, history, debugging and workspace management. We used Rstudio and generated this document with R Markdown. R Markdown is designed for easier reproducibility, because both computing code and narratives are in the same document. The code runs with the “dplyr”-package. The below example refers to the 2018 data as shown by the file names, but the code works with any other service value matrix in .csv-format as long as it is properly structured.

Basically, three steps are explained in this brief guide: (i) creating a numerical service value matrix; (ii) computing the inter-city connectivity matrix and (iii) generating a table with global network connectivities.

Step 1 - Creating a numerical service value matrix

First of all, GaWC’s two-mode service value matrix needs to be read and stored. Data are stored in a dataframe called ‘svm’ with the following code:

svm <- read.csv2("GaWC_svm_18.csv", header=TRUE, sep=",")

A dataframe can contain characters, strings and numbers, and is therefore not fit for matrix algebra. We extract the cities and firms from the dataframe and transform what is left into a numerical matrix ‘svm_mat’ (dimensions: 175 firms x 707 cities) as follows:

Cities <- svm[,"City"]
Firms <- colnames(svm)[-c(1:3)]
svm <- svm[,-c(1:3)]
row.names(svm) <- Cities
svm_mat <- data.matrix(svm, rownames.force=TRUE)

Step 2 - Constructing inter-city connectivity matrix

The icc matrix is basically the product of the svm matrix and its transpose (Derudder, 2020). This can easily be done with the tcrossprod-function. Keep in mind that the diagonals are zero.

res <- tcrossprod(svm_mat, y=NULL)
diag(res) <- 0

Step 3 - Calculating global network connectivity for every city

To calculate absolute and relative global network connectivity for every city, we use code that calculates the total icc-value for every city (which is the absolute GNC-value), and sorts the output. We add a GNC_rel value and a rank to the table.

GNC <- sort(rowSums(res), decreasing=TRUE)
Cities2 <- names(GNC)
df <- data.frame(Cities2, GNC)
names(df) <- c("City","GNC_abs")
df_mut <- mutate(df, GNC_rel=round(GNC/max(GNC), 3), rank = dense_rank(desc(df$GNC_abs)))

^* Tom Storme and Ben Derudder, SEG Research Group, Ghent University, 1 April 2020