# Hierarchical Cluster Analysis and Node Centrality Scores for Industrial Symbiosis Network models of Point Lisas Industrial Estate

## Description

This dataset contains processed experimental simulation data supporting the results of the unfunded study titled “Filtering ‘3-2’ Industrial Symbiosis Networks at a Carbon-Intensive Cluster in a Small Island Developing State to Reuse CO2 and Water”. The data was processed using the algorithms and software described in the Methods section of that study (https://doi.org/10.1016/j.cherd.2024.10.023). To investigate the industrial symbiosis (IS) for combined carbon dioxide utilization and water reuse on the Point Lisas Industrial Estate (PLIE), enterprise input-output MILP models of a representative IS network were developed. Discarded water streams with multiple contamination levels and high-purity process CO2 from ammonia processes were selected as materials to be reused in: existing petrochemical plants, a mineral carbonate factory and a propylene carbonate plant. The relative locations of these plants is reported. Firstly, exploratory hierarchical cluster analysis (HCA) was performed to discover summary knowledge of the chosen cluster model (e.g. the likely number of subclusters) with the Python library, SciPy using agglomerative clustering. The cophenetic correlation coefficient and dendrograms from the HCA with different linkage functions are reported. Then economic and environmental objectives were set for each material. Combining economic objectives left a tri-objective problem, which was resolved with ε-constraint optimization and multi-criteria decision-making methods, for two different scenarios - with and without the mineral carbonate and propylene carbonate plants. Graph and network algorithm functions in MATLAB® (ver. R2021a) were used to create network graphs from weighted and directed adjacency matrices, which contained the magnitude and direction of inter-plant flows, and then calculate network metrics that characterize structural attributes, in particular five centrality indices: degree, closeness, betweenness, 'hubs' and 'authorities' were calculated using MATLAB’s centrality function. Along with network connectance, the 'in' and 'out' degree, 'in' and 'out' closeness, betweenness, Kleinberg's 'hub' and 'authority' centrality scores are reported for the individual and combined networks for both scenarios.

## Files

## Steps to reproduce

Hierarchical Cluster Analysis The plant positional coordinates were put in a matrix to perform hierarchical cluster analysis (HCA). This was passed to the Python hierarchical clustering linkage function, scipy.cluster.hierarchy.linkage, in the library SciPy, which was called with the metric set to 'euclidean' and the method first set to 'single'. The matrix of actual inter-nodal distances and the matrix of distances predicted by the HCA were passed to the function scipy.cluster.hierarchy.cophenet, which returned the cophenetic correlation coefficient. Then the HCA matrix was plotted as a dendrogram. Finally, this procedure was than repeated with the linkage method set to 'ward'. Node Centrality Measures For a given material (carbon dioxide or water) or the sum of both materials, a simple directed weighted-edge graph was created from the plant positional coordinates and the material flows between node pairs from the optimal solution for the scenario without the mineral carbonate and propylene carbonate plants (Scenario 1). Disconnected nodes were removed from graph, which was then plotted with MATLAB plot function. The graph density or connectance was calculated. Using adjacency matrices, self-loops were stripped from the graph and the connectance was recalculated. Then self-loopless weighted-edge graph was passed repeatedly to MATLAB centrality function to calculate in turn: 'outdegree', 'outcloseness', 'indegree', 'incloseness', 'betweenness' ,'hubs' and 'authorities'. This procedure was repeated for the same material from the optimal solution for the scenario with the mineral carbonate and propylene carbonate plants (Scenario 2). For each material-scenario set, the degree, closeness and betweenness indices were normalised to sum to 1 in a spreadsheet.