Figure 1.
(a) Degree Centrality. (b) Betweenness Centrality. (c) Closeness Centrality. (d) Eccentricity Centrality. (e) Eigenvector Centrality.
Figure 2.
Figure 2 represents the Erdös–Rnyi network formed with the p = 0.1. The network consists of a source, target and intermediate laid randomly in the network. Figure 2a represents the degree centrality of the individual nodes according to the size and color variation. Nodes (blue) have the highest degree centrality and thus have the largest size in the network where as the nodes (red) have the smallest value of degree centrality in the network. Figure 2b represents betweenness centrality of the nodes in the network. Nodes (blue) have the highest betweenness centrality and have the largest size in the network as the betweenness value decreases so the size and also the color changes ultimately to red. Figure 2c and figure 2d represents closeness centrality and eccentricity centrality of nodes of this network. Both of the centralities are analyzed on this network, the highest value nodes are represented as the largest nodes in blue color. To see the central node in the network or to observe which node is most eccentric in the network, reciprocal of these values is taken. Here, smaller the size of a node is more central and eccentric in the network. Figure 2e represents the eigenvector centrality of the nodes in the network. The highest value nodes are represented in blue color where as nodes with lowest values are represented in red color. (a) Degree Centrality. (b) Betweenness Centrality. (c) Closeness Centrality. (d) Eccentricity Centrality. (e) Eigenvector Centrality.
Figure 3.
Zachary's Karate Club Network.
Figure 3 represents Zachary's Karate Club network. The network is laid out randomly representing source and intermediate nodes as club instructor, club president and officers in the network. Club instructor and club president either of them is considered to be a source node of information flow in the network. Figure 3a represents the degree centrality of the individual nodes according to the size and color variations. Nodes in blue color have the highest degree centrality and thus have the largest size in the network where as nodes in red color have the least value of degree centrality. Figure 3b represents betweenness centrality of the nodes in the network. Nodes (blue) have the highest betweenness centrality and have the largest size in the network as the betweenness value decreases so the size and also the color changes ultimately to red. Figure 3c and figure 3d represents closeness centrality and eccentricity centrality respectively. Both of the centralities analyzed on the network show that the highest value nodes are represented as the largest nodes in blue color. To see the central node in the network or to observe which node is most eccentric in the network, reciprocal of these values is taken. Here, smaller the size of a node is more central and eccentric in the network figure 3e represents the eigenvector centrality of the nodes in the network. Nodes represented in blue color have the highest value where as nodes with lowest values are represented in red color. (a) Degree Centrality. (b) Betweenness Centrality. (c) Closeness Centrality. (d) Eccentricity Centrality. (e) Eigenvector Centrality.
Figure 4.
Figure 4 represents Dolphins social network. The details of the nodes identity are not given in the originally compiled data, therefore we assume the network laid out randomly consists of source, target and intermediate nodes. Figure 4a represents the degree centrality of the individual nodes according to the size and color variation. Nodes (blue) have the highest degree centrality and thus have the largest size in the network where as nodes (red) have the least value of degree centrality in the network. Figure 4b represents betweenness centrality of the nodes in the network. Nodes (blue) have the highest betweenness centrality and have the largest size in the network as the betweenness value decreases so the size and also the color changes ultimately to red. Figure 4c and figure 4d represents closeness centrality and eccentricity centrality of this social network. Both of the centralities analyzed for the network have the highest value nodes represented as the largest nodes in blue color. To see the central node in the network or to observe which node is most eccentric in the network, reciprocal of these values is taken. Here, smaller the size of a node is more central and eccentric in the network. Figure 4e represents the eigenvector centrality of the nodes in this social network. Nodes in blue color have the highest value of centrality where as nodes with lowest value are represented in red color. (a) Degree Centrality. (b) Betweenness Centrality. (c) Closeness Centrality. (d) Eccentricity Centrality. (e) Eigenvector Centrality.
Figure 5.
Figure 5 represents a neural network of nematode Caenorhabditis elegans. The details of the nodes identity are not given by the source from which the data has been collected therefore we assume the network laid out randomly consists of source, target and intermediate nodes. Figure 5a represents the degree centrality of the individual nodes according to the size and color variation. Nodes (blue) have the highest degree centrality and thus have the largest size in the network where as nodes (red) have the least value of degree centrality in the network. Figure 5b represents betweenness centrality of the nodes in the network. Nodes (blue) have the highest betweenness centrality and have the largest size in the network as the betweenness value decreases so the size and also the color changes ultimately to red. Figure 5c and figure 5d represents closeness centrality and eccentricity centrality of this neural network. Both of the centralities analyzed for the network have the highest value nodes represented as the largest nodes in blue color. To see the central node in the network or to observe which node is most eccentric in the network, reciprocal of these values is taken. Here, smaller the size of a node is more closer and eccentric in the network. Figure 5e represents the eigenvector centrality of the nodes in the network. The highest value nodes are represented in blue color where as nodes with lowest values are represented in red color. (a) Degree Centrality. (b) Betweenness Centrality. (c) Closeness Centrality. (d) Eccentricity Centrality. (e) Eigenvector Centrality.
Figure 6.
The graphs show a correlation between the frequency of the nodes and the centrality in the Erdös–Rnyi model network with n = 50.
Figure 6a shows the Degree Centrality; there are 2 nodes having maximum value and other 3 nodes having the minimum value
. Figure 6b shows the Betweenness Centrality; there is only one node having maximum value
and 8 nodes having the minimum value
. Figure 6c shows the Closeness Centrality; there is only one node having maximum value
and one node having the minimum value
. Figure 6d shows the Eccentricity Centrality; there are 9 nodes having maximum value
and 3 nodes having the minimum value
. Figure 6e shows the Eigenvector Centrality; there is only one node having maximum value
and only one node having the minimum value
. (a) Degree Centrality. (b) Betweenness Centrality. (c) Closeness Centrality. (d) Eccentricity Centrality. (e) Eigenvector Centrality.
Figure 7.
In the Zachary's Karate Club network, the graphs show a correlation between the frequency of the nodes and the centrality in the karate club network with n = 34.
Figure 7a shows the Degree Centrality; there are 2 nodes having maximum value and only one node having the minimum value
. Figure 7b shows the Betweenness Centrality; there is only one node having maximum value
and 19 nodes having the minimum value
. Figure 7c shows the Closeness Centrality; there are 7 nodes having maximum value
and one node having minimum value
. Figure 7d shows the Eccentricity Centrality; there are 8 nodes having maximum
and 9 nodes having the minimum value
. Figure 7e shows the Eigenvector Centrality; there are 2 nodes having maximum value
and only one node having the minimum value
. (a) Degree Centrality. (b) Betweenness Centrality. (c) Closeness Centrality. (d) Eccentricity Centrality. (e) Eigenvector Centrality.
Figure 8.
In the Dolphin Social Network, the graphs show a correlation between the frequency of the nodes and the centrality in the dolphin social network with n = 62.
Figure 8a shows the Degree Centrality; there is only one node having maximum value and 9 nodes having the minimum value
. Figure 8b shows the Betweenness Centrality; there is only one node having maximum value
and 22 nodes having the minimum value
. Figure 8c shows the Closeness Centrality; there are 4 nodes having maximum value
and only one node having the minimum value
. Figure 8d shows the Eccentricity Centrality; there are 10 nodes having maximum value
and 8 nodes having the minimum value
. Figure 8e shows the Eigenvector Centrality; there is only one node having maximum value
and 22 nodes having the minimum value
. (a) Degree Centrality. (b) Betweenness Centrality. (c) Closeness Centrality. (d) Eccentricity Centrality. (e) Eigenvector Centrality.
Figure 9.
In the neural network, the graphs show a correlation between the frequency of the nodes and the centrality in the neural network with n = 297.
Figure 9a shows the Degree Centrality; there is only one node having maximum value and 250 nodes having the minimum value
. Figure 9b shows the Betweenness Centrality; there is only one node having maximum value
and 258 nodes having the minimum value
. Figure 9c shows the Closeness Centrality; there are 10 nodes having maximum value
and 37 nodes having the minimum value
. Figure 9d shows the Eccentricity Centrality; there are 60 nodes having maximum value
and 9 nodes having the minimum value
. Figure 9e shows the Eigenvector Centrality; there are 13 nodes having maximum value
and 56 nodes having the minimum value
.
Table 1.
Centralities Effect on Information Diffusion.