Measure of Connectivity-Degree Centrality
Degree centrality is the simplest form of centrality measures for networks. Although it is very simple, it has a great significance. It represents the connectivity of a node to the network . Individuals who have more links with other persons are more connected to the network in the sense that they have more resource, access of information than others. A nonsocial network example is the use of citation counts in the evaluation of scientific papers. The number of citations of a paper can be regarded as its impact on research . For example, node 2 in Fig. 1 is adjacent to four other nodes, it’s degree is four. In a 5 node graph, any node can be adjacent to only remaining four nodes. So, this node has got highest connectivity. In some literature studies, degree centrality is defined as:
where, degðkÞ is the degree of node k. In case of electrical network, the power flowing in the adjacent links of the node in concern can be regarded as a degree of the node and the definition of the electrical degree centrality can be given as:
where, k rv t indicates that node k are t are connected. Pkt indicates the power flowing in line connected in between nodes k and t. Table 2 shows the degree centrality of simple 5 bus system in Fig. 1 using classical and proposed approach.