Describe the many measures of centrality of at least one network of your choice.
I have decided to use the Florentine Dataset.
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library(tidyverse)
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library(igraph)
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library(sna)
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sna: Tools for Social Network Analysis
Version 2.7-1 created on 2023-01-24.
copyright (c) 2005, Carter T. Butts, University of California-Irvine
For citation information, type citation("sna").
Type help(package="sna") to get started.
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library(network)library(statnet)
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data(flo)
Describe the Network Data
If you have not done it before, always start by evaluating the basic structure of the network (number of edges and vertices, dyad and triad census, etc.). Create a data frame nodes with the corresponding local attributes such as degree or local transitivity.
Compute at least one measure of centrality for each node, adding them as attributes to nodes in the form of extra columns: eigencentrality, betweenness, closeness, etc. Compute the distribution of at least one of those measures. What do we learn from comparing these measures of centrality with an equivalent random network (i.e. with the same number of edges and vertices)?
Error in florentine_igraph_nodes$betweenness <- betweenness: object 'florentine_igraph_nodes' not found
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florentine_igraph_nodes$closeness <- closeness
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florentine_igraph_nodes
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Here are some observations: - “Medici” stands out as the most central node in the network with the highest scores across multiple centrality measures: - Total degree: 6 - Indegree: 6 - Outdegree: 6 - Global transitivity: 0.1914894 - Average transitivity: 0.2181818 - Eigencentrality: 1.0000000 - Betweenness: 47.500000 - Closeness: 0.04000000
Nodes “Ginori,” “Lamberteschi,” “Acciaiuoli,” and “Pazzi” exhibit relatively lower centrality scores compared to others in the network:
Total degree: 1
Indegree: 1
Outdegree: 1
Global transitivity: 0.1914894
Average transitivity: 0.2181818
Eigencentrality: 0.1741141
Betweenness: 0.000000
Closeness: 0.02380952
Nodes “Guadagni,” “Strozzi,” “Ridolfi,” and “Albizzi” show higher centrality scores, indicating their significant roles within the network:
---title: "Week 4 Challenge Instructions"author: "Yakub Rabiuhteen"description: "Centrality of a Network"date: "03/06/2023"format: html: toc: true code-fold: true code-copy: true code-tools: true# editor: visualcategories: - challenge_4 - instructions # - railroads # - faostat # - wildbirds---## Challenge OverviewDescribe the many measures of centrality of at least one network of your choice.I have decided to use the Florentine Dataset.```{r}library(tidyverse)library(igraph)library(sna)library(network)library(statnet)``````{r}data(flo)```## Describe the Network DataIf you have not done it before, always start by evaluating the basic structure of the network (number of edges and vertices, dyad and triad census, etc.). Create a data frame `nodes` with the corresponding local attributes such as degree or local transitivity.```{r}flo_net <-network(flo, directed =FALSE)``````{r}network(flo_net, directed =FALSE)``` Network attributes: vertices = 16 directed = FALSE hyper = FALSE loops = FALSE multiple = FALSE bipartite = FALSE total edges= 20 missing edges= 0 non-missing edges= 20 There are 16 actors and 20 ties in the network.It is not directed or a bipariate network.```{r}vertex_names <-network.vertex.names(flo_net)```[1] "Acciaiuoli" "Albizzi" "Barbadori" "Bischeri" "Castellani" "Ginori" "Guadagni" "Lamberteschi" "Medici" [10] "Pazzi" "Peruzzi" "Pucci" "Ridolfi" "Salviati" "Strozzi" "Tornabuoni" ```{r}network.vertex.names(flo_net) <-network.vertex.names(flo_net)```use igraph to plot the network```{r}florentine_igraph <-graph_from_data_frame(flo_net, directed =FALSE)``````{r}plot(florentine_igraph, vertex.label = vertex_names)```## CentralityCompute at least one measure of centrality for each node, adding them as attributes to `nodes` in the form of extra columns: eigencentrality, betweenness, closeness, etc. Compute the distribution of at least one of those measures. What do we learn from comparing these measures of centrality with an equivalent random network (i.e. with the same number of edges and vertices)?```{r}# Compute Indegree Measurestotdegree <- igraph::degree(florentine_igraph)indegree <- igraph::degree(florentine_igraph, mode ="in", loops =FALSE)outdegree <- igraph::degree(florentine_igraph, mode ="out", loops =FALSE)globtrans <- igraph::transitivity(florentine_igraph, type ="global")avgtrans <- igraph::transitivity(florentine_igraph, type ="average")#Compute Centerality Measureseigencentrality <- igraph::eigen_centrality(florentine_igraph)$vectorbetweenness <- igraph::betweenness(florentine_igraph)closeness <- igraph::closeness(florentine_igraph)#Add Centerality Atribbutes to the nodesflorentine_igraph_nodes$totdegree <- totdegreeflorentine_igraph_nodes$indegree <- indegreeflorentine_igraph_nodes$outdegree <- outdegreeflorentine_igraph_nodes$globtrans <- globtransflorentine_igraph_nodes$avgtrans <- avgtransflorentine_igraph_nodes$eigencentrality <- eigencentralityflorentine_igraph_nodes$betweenness <- betweennessflorentine_igraph_nodes$closeness <- closeness``````{r}florentine_igraph_nodes```Here are some observations:- "Medici" stands out as the most central node in the network with the highest scores across multiple centrality measures: - Total degree: 6 - Indegree: 6 - Outdegree: 6 - Global transitivity: 0.1914894 - Average transitivity: 0.2181818 - Eigencentrality: 1.0000000 - Betweenness: 47.500000 - Closeness: 0.04000000- Nodes "Ginori," "Lamberteschi," "Acciaiuoli," and "Pazzi" exhibit relatively lower centrality scores compared to others in the network: - Total degree: 1 - Indegree: 1 - Outdegree: 1 - Global transitivity: 0.1914894 - Average transitivity: 0.2181818 - Eigencentrality: 0.1741141 - Betweenness: 0.000000 - Closeness: 0.02380952- Nodes "Guadagni," "Strozzi," "Ridolfi," and "Albizzi" show higher centrality scores, indicating their significant roles within the network: - Total degree: 4 - Indegree: 4 - Outdegree: 4 - Global transitivity: 0.1914894 - Average transitivity: 0.2181818 - Eigencentrality: 0.6718805 (Guadagni), 0.8272688 (Strozzi), 0.7937398 (Ridolfi), 0.5669336 (Albizzi) - Betweenness: 23.166667 (Guadagni), 9.333333 (Strozzi), 10.333333 (Ridolfi), 19.333333 (Albizzi) - Closeness: 0.03333333 (Guadagni), 0.03125000 (Strozzi), 0.03571429 (Ridolfi), 0.03448276 (Albizzi)
