In this project, we use leverage of centrality models for extracting the importance of network graph in some determined topologies. The aim is to have scrutinizing and analyzing the centralities in different network topologies. Three type of centrality that are used in this project are Betweenness, Closeness and eigenvector one. Moreover, we have show the results of this comparison in the experimental results. Besides, we have extend the results of our experimental works for real world problems. The Results of this part are grasped with visualization plots for some centralities measurements clearly.

1. CENTRALITY OF GRAPH ON DIFFERENT NETWORK TOPOLOGIES
Aydin Ayanzadeh
Department of Computer Engineering, Istanbul Technical University.
Abstract
In this project, we use leverage of centrality models for extracting the importance
of network graph in some determined topologies. The aim is to have scrutinizing
and analyzing the centralities in different network topologies. Three type of cen-
trality that are used in this project are Betweenness, Closeness and eigenvector
one. Moreover, we have show the results of this comparison in the experimental
results. Besides, we have extend the results of our experimental works for real
world problems. The Results of this part are grasped with visualization plots for
some centralities measurements clearly.
FIGURE 1
Visualization of different centrality on extended star graph.
INTRODUCTION
Analyzing data with visual methods helps us to have better vision
about the complexity of our application.Actually, this scrutinizing
helps us to watch the ecosystems of our networks with better per-
spective. This evaluation are very helpful different application of
the network such as clustering, routing of the packets and classifi-
cation of the network traffic and etc.
For evaluating the performance of our application in the network,
we have to find the some static and dynamic measures of given
graph for increasing the accuracy and error loss of the packet dur-
ing the routing among the nodes. For optimizing the over network
we have to some essential measures that help us to reach this ap-
proach. In our application, we can find some essential measures
for each graph networks such as shortest path, centerness, close-
ness and etc. In advance level we can also find some additional
measures for each nodes of networks and some public measures
such as diameter and other related measures that are related the
graphs in the networks. For evaluating and analyzing our applica-
tion we create numbers of graph with special features(complicated,
tree and etc.) and analyze the related measures in that graph. Fig1
is the visualization of simple graph that the right one is correspond
to the star graph and other one is a simple graph with characteristic
features.
FIGURE 2
METHODS
For Calculating and finding the centrality of determined graph we
utilize the different type of centrality measures such as Katz, Eigen-
vector, Betweenness and closeness centrality.
RESULTS
We apply different measures of centrality on different network
topologies for showing that each network should be evaluated with
own centrality method. For grasping our work, we apply four type
of network topologies. The used topologies are Star graph,Tree,
Fully connected and extended star graph. The visualization of our
works are enclosed in Fig1, Fig2,Fig3 and Fig4 .
If we want to finding very connected individuals, popular peo-
ple( in social networks), individuals who are likely to hold most
among other nodes, degree centrality suggested.
If we need to have further process among the nodes with
the policy of degree centrality eigenvalue centrality is sug-
gested(suitable for more complicated networks).
Hence, all of the centrality measures give effective results for
our networks(but each measure give different impact for each
node in determined graph).
FIGURE 3
Visualization of different centrality on star graph.
CONCLUSION
According to the abovementioned, we can reaching an agreement
that one centrality method is not comprehensive enough for all of
network topologies. Hence, we need to calculate all of the cen-
trality techniques for find the best one among the state-of-the-art
methods. In some topologies we do not have true results based on
the determined results.
REFERENCE
Newman, Mark. Networks: An Introduction (pp. 168-234,
Chapter 7: Measures and Metrics)., Oxford University Press,
2010.