Graphs & Index Calculations Canada (PII)

Based on Concepts around SMRs - draft4

Objective

This file continues the work of the previous file PI. It was created to calculate modularity and E-I index based on igraph package for the networks build on each concept. We focus only on the concepts that counts for the 99% of the sample (see Research Note 43 - DNA Canada Analysis complements):

# code Nodes Links % Text
1 c55 91 2799 26.7 solution to environmental
2 c38 68 1414 40.1 efficient electricity production
3 c615 64 1237 51.9 new opportunity
4 c54 51 757 59.1 safe for humans
5 c30 45 756 66.3 boost to exports and economic growth
6 c52 41 742 73.4 smaller grids
7 c638 47 739 80.4 part of an energy mix
8 c58 32 388 84.1 technological leadership
9 c41 31 384 87.8 generates employment
10 c719 34 291 90.6 waste is manageable
11 c50 26 165 92.1 reasonable cost
12 c628 21 156 93.6 international trend
13 c32 18 153 95.1 SMRs progress
14 c36 21 142 96.4 needs to be regulated
15 c618 17 106 97.4 SMRs
16 c849 18 66 98.1 growing acceptance of nuclear
17 c644 21 46 98.5 add value to uranium
18 c621 16 45 98.9 produces heat

Coalitions by Concept

We need to

##Building graphs

After getting the matrices, we build the graphs based on igrpah

##Plotting graphs At this point we have finished the procedure of transforming adjacency matrices in graphs and we have added the attributes. We are ready to plot the graphs.

Index calculations

Using different packages we calculate the modularity index.

Modularity

Modularity measures coalition polarization. It ranges from 0 to 1.

  • Values close to 0 mean shows low polarization between groups. And there differences within each coalition

  • Values close to 0.5 do not show any association.

  • Values close to 1 show high polarization between groups. Coalitions are compacted internally and show a great difference to others coalitions.

GraphName Modularity
grafo30 0.0388952
grafo32 0.0000000
grafo36 0.0809363
grafo38 0.1930345
grafo41 0.0191956
grafo50 0.3966942
grafo52 0.0026918
grafo54 0.2115212
grafo55 0.1026251
grafo58 0.0300776
grafo615 0.2298096
grafo618 0.0186899
grafo621 0.0000000
grafo628 0.0377219
grafo638 0.0926828
grafo644 0.0425331
grafo719 0.4240089
grafo849 0.3378099

Average modularity is 0.125496

Within and Between densities

```{r within and between community density, echo=FALSE}

Within and between community edge density

Concept Community WithinDensity BetweenDensity
grafo30 1 0.2417632 0.0000000
grafo30 2 0.1719577 0.0000000
grafo32 1 0.2903476 0.0000000
grafo36 1 0.4592525 0.0000000
grafo36 2 0.4861111 0.0000000
grafo38 1 0.2598662 0.0141031
grafo38 2 0.2669208 0.0141031
grafo38 3 0.0000000 0.0141031
grafo41 1 0.3237963 0.0503282
grafo41 2 0.0000000 0.0503282
grafo41 3 0.2250000 0.0503282
grafo50 1 0.2916667 0.0000000
grafo50 2 0.4011111 0.0000000
grafo52 1 0.2730656 0.0000000
grafo52 2 0.2000000 0.0000000
grafo54 1 0.2528682 0.0000000
grafo54 2 0.2564268 0.0000000
grafo55 1 0.1427568 0.0011925
grafo55 2 0.1083552 0.0011925
grafo58 1 0.1934061 0.0027636
grafo58 2 0.1547619 0.0027636
grafo615 1 0.2717378 0.0254807
grafo615 2 0.2666905 0.0254807
grafo615 3 0.0000000 0.0254807
grafo615 4 0.0000000 0.0254807
grafo618 1 0.4614286 0.0000000
grafo618 2 0.3500000 0.0000000
grafo621 1 0.4455556 0.0000000
grafo628 1 0.5806100 0.0000000
grafo628 2 0.5000000 0.0000000
grafo638 1 0.1438492 0.0000000
grafo638 2 0.1864445 0.0000000
grafo644 1 0.8000000 0.0000000
grafo644 2 0.7500000 0.0000000
grafo719 1 0.2655782 0.0174823
grafo719 2 0.2571086 0.0174823
grafo719 3 0.0000000 0.0174823
grafo849 1 0.8055556 0.0571429
grafo849 2 0.7500000 0.0571429