It gives background information into your topic area and outlines all the ideas you are going to present.
An introduction to Centrality measures Figure 1: Some questions to ponder: If I need to recruit 10 people for my newly found organization, whom should I consider? If I am to pass on a message to three people in this network so that they in turn convey it to their friends and so on.
Which three people should I select?
If I am to rank all my friends based on how "central" they are in this network, how would I go about? If I were to nominate a leader for this team ofwhom should I pick?
Any more questions that we could ask? When and how to term a vertex important? Is the vertex which has maximum degree obviously the most important vertex? If the network denoted a road network in a city and if there was a vertex connecting and hence bridging the two big components, would you not term this new vertex as the most important one?
A vertex adjacent to other vertices which are all pendant, is intuitively considered better ranked than a vertex which has 50 adjacent vertices each of degree This is a question that will motivate us to study how Google crawls and ranks the pages on the WWW.
There is a clear call for formalism! Unfortunately, there is not much formal definition of centrality indices, but the following two features: A vertex centrality is a real-valued function assigning to each vertex in a network some value.
The higher the value, the more central the vertex is for the network whatever the definition of centrality used. If two graphs G, H are isomorphic and p v denotes the mapping function from a node v in G to some node v' in H, then centrality v in G needs to be the same as centrality p v in H.
In other words, we require that the centrality of a vertex is ONLY depending on the structure of the graph and no other contextual information. Centrality Measures We will start with four different centrality measures: For an interesting application of degree centrality, take a look at Jeong et al.
Betweenness centrality is less obvious to compute try doing it manually for a random graph on 8 vertices Below is an interesting example of two regular graphs one which is symmetric and the other one isn't.
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