## 3 Sociocentric and Egocentric Centrality Measures
### Egocentric Centrality Measures
\begin{tabular}{c c c c c c c c}  & W4 & I1 & S1 & W3 & W1 & W2 & W5 \\ W4 & I1 & & 1 & 1 & 1 & 1 & 1 \\ I1 & & 0 & 0 & 1 & 1 & 1 & 0 \\ S1 & & 0 & 0 & 1 & 1 & 1 & 1 \\ W4 & = W3 & 1 & 1 & 1 & 0 & 1 & 1 \\ W1 & & 1 & 1 & 1 & 0 & 1 & 1 \\ W2 & 1 & 1 & 1 & 1 & 1 & 0 & 0 \\ W5 & 1 & 0 & 1 & 1 & 1 & 0 & 0 \\ \end{tabular}   
Since the adjacency matrix \(W4\) is symmetric and according to Equation (4), only the non-zero values above the primary diagonal need to be analysed (\(i<j\)). In this case, the remaining entries of \(W4^{2}[1-W4]\) are 4, 3 and 4, as shown in the matrix below. \begin{tabular}{c c c c c c c} W4 & I1 & S1 & W3 & W1 & W2 & W5 \\ I1 & & * & * & * & * & * & * \\ S1 & & * & * & * & * & * & * \\ S & * & * & * & * & * & * \\ S & * & * & * & * & * & * \\ W1 & & * & * & * & * & * & * \\ W2 & * & * & * & * & * & * & 4 \\ W5 & * & * & * & * & * & * & * \\ \end{tabular}   
Therefore, the egocentric betweenness score of the ego node \(W4\) is 0.83 (\(1/4+1/3+1/4\)). In this way, by using only the local knowledge available, each node can compute its egocentric betweenness score. Table 1 shows the scores of all nodes from the example of Figure 2, based on both betweenness centrality measures. Since egocentric betweenness is computed over the geodesic paths of the maximal length of two, the scores found in the egocentric betweenness measure are usually smaller than their sociocentric equivalents. However, an observation that is important to highlight is the similarity ranking of nodes. The illustrative example given here was based on static networks; however, one of our major challenges is to perform the same calculation in highly dynamic network scenarios such as VANETs. In these networks, the egocentric betweenness score should be updated whenever a new communication link is established or when a communication link ceases to exist. To exemplify how each node behaves and how the network structure can change in a highly dynamic network scenario, in relation to the betweenness centrality score, a set of footprints that \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{3}{c}{**Betweenness Centrality**} \\ \hline  & **Sociocentric** & **Egocentric** \\ \hline  & W1 & 3.75 & 0.83 \\  & W2 & 0.25 & 0.25 \\  & W3 & 3.75 & 0.83 \\  & W4 & 3.75 & 0.83 \\  & W5 & 30.00 & 4.00 \\  & W6 & 0.00 & 0.00 \\ Nodes & W7 & 28.33 & 4.33 \\  & W8 & 0.33 & 0.33 \\  & W9 & 0.33 & 0.33 \\  & S1 & 1.50 & 0.25 \\  & S2 & 0.00 & 0.00 \\  & S4 & 0.00 & 0.00 \\  & I1 & 0.00 & 0.00 \\  & I3 & 0.00 & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Egocentric and sociocentric betweenness scores of Figure 2.  
describe a frame sequence (Figure 3) was illustrated; see Figure 3a-c. It shows the behaviour of the network topology (or temporal graphs) through a heat map set of our experiment scenario that will be presented later. The density is 150 vehicles/km\({}^{2}\), and the transmission range is 200 m. Each node (or vehicle) is represented by a circle, and every communication link is represented by a bar. Moreover, each node can have five different colours according to the betweenness centrality score, ranging from low to high, as shown in Figure 3.