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How the degree centrality measure changes in the presence of loops?

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0

$begingroup$

I am using R with the igraph package to make some experiment. In particular I am making a star graph. So I build a graph with 5 nodes, 4 of them connected to the central node and nothing else:

library(igraph)
g = make_star(5, mode="undirected")

The above graph obviously contains no loops. Running:

centr_degree(g, loops=F, normalized=F)

Gives the correct result:

$`res`
[1] 4 1 1 1 1

$centralization
[1] 12

$theoretical_max
[1] 12

Where $res is the vector of centrality of each node, $centralization is the centralization for the entire graph using Freeman centralization formula, and $theoretical_max is the theoretical maximum centrality of a network (so, again, Freeman centrality) with the same number of nodes and the same configuration.

For degree centrality, the network with the maximum Freeman's degree centrality is the star network that I just built. So, correctly, $centralization == $theoretical_max

But running
centr_degree(g, loops=T, normalized=T)

Changes the theoretical maximum

$`res`
[1] 4 1 1 1 1

$centralization
[1] 12

$theoretical_max
[1] 20

And of course the value if you normalize too:

> centr_degree(g, loops=T, normalized=T)
$`res`
[1] 4 1 1 1 1

$centralization
[1] 0.6

$theoretical_max
[1] 20

Questions:

1. How does the calculation of the degree centrality for the network changes if you introduce loops? That is, why the theoretical maximum raises?




2. Is it correct that the normalized version changes, even if my network does not have loops?

graph-theory network

share|cite|improve this question

asked Mar 15 at 18:26

raffamaidenraffamaiden

1156

$endgroup$

add a comment | 

0

$begingroup$

I am using R with the igraph package to make some experiment. In particular I am making a star graph. So I build a graph with 5 nodes, 4 of them connected to the central node and nothing else:

library(igraph)
g = make_star(5, mode="undirected")

The above graph obviously contains no loops. Running:

centr_degree(g, loops=F, normalized=F)

Gives the correct result:

$`res`
[1] 4 1 1 1 1

$centralization
[1] 12

$theoretical_max
[1] 12

Where $res is the vector of centrality of each node, $centralization is the centralization for the entire graph using Freeman centralization formula, and $theoretical_max is the theoretical maximum centrality of a network (so, again, Freeman centrality) with the same number of nodes and the same configuration.

For degree centrality, the network with the maximum Freeman's degree centrality is the star network that I just built. So, correctly, $centralization == $theoretical_max

But running
centr_degree(g, loops=T, normalized=T)

Changes the theoretical maximum

$`res`
[1] 4 1 1 1 1

$centralization
[1] 12

$theoretical_max
[1] 20

And of course the value if you normalize too:

> centr_degree(g, loops=T, normalized=T)
$`res`
[1] 4 1 1 1 1

$centralization
[1] 0.6

$theoretical_max
[1] 20

Questions:

1. How does the calculation of the degree centrality for the network changes if you introduce loops? That is, why the theoretical maximum raises?




2. Is it correct that the normalized version changes, even if my network does not have loops?

graph-theory network

share|cite|improve this question

asked Mar 15 at 18:26

raffamaidenraffamaiden

1156

$endgroup$

add a comment | 

$begingroup$

I am using R with the igraph package to make some experiment. In particular I am making a star graph. So I build a graph with 5 nodes, 4 of them connected to the central node and nothing else:

library(igraph)
g = make_star(5, mode="undirected")

The above graph obviously contains no loops. Running:

centr_degree(g, loops=F, normalized=F)

Gives the correct result:

$`res`
[1] 4 1 1 1 1

$centralization
[1] 12

$theoretical_max
[1] 12

Where $res is the vector of centrality of each node, $centralization is the centralization for the entire graph using Freeman centralization formula, and $theoretical_max is the theoretical maximum centrality of a network (so, again, Freeman centrality) with the same number of nodes and the same configuration.

For degree centrality, the network with the maximum Freeman's degree centrality is the star network that I just built. So, correctly, $centralization == $theoretical_max

But running
centr_degree(g, loops=T, normalized=T)

Changes the theoretical maximum

$`res`
[1] 4 1 1 1 1

$centralization
[1] 12

$theoretical_max
[1] 20

And of course the value if you normalize too:

> centr_degree(g, loops=T, normalized=T)
$`res`
[1] 4 1 1 1 1

$centralization
[1] 0.6

$theoretical_max
[1] 20

Questions:

1. How does the calculation of the degree centrality for the network changes if you introduce loops? That is, why the theoretical maximum raises?




2. Is it correct that the normalized version changes, even if my network does not have loops?

graph-theory network

share|cite|improve this question

asked Mar 15 at 18:26

raffamaidenraffamaiden

1156

$endgroup$

$`res`
[1] 4 1 1 1 1

$centralization
[1] 12

$theoretical_max
[1] 12

$`res`
[1] 4 1 1 1 1

$centralization
[1] 12

$theoretical_max
[1] 20

> centr_degree(g, loops=T, normalized=T)
$`res`
[1] 4 1 1 1 1

$centralization
[1] 0.6

$theoretical_max
[1] 20

share|cite|improve this question

asked Mar 15 at 18:26

raffamaidenraffamaiden

1156

share|cite|improve this question

asked Mar 15 at 18:26

raffamaidenraffamaiden

1156

asked Mar 15 at 18:26

raffamaidenraffamaiden

1156

asked Mar 15 at 18:26

raffamaidenraffamaiden

1156