The Classification of random graph models using graph centralities

Abstract

In this paper, a classification method of random graph models is proposed and it is based on centralities of the random graphs. Similarity between two random graphs is measured for the classification of random graph models. The similarity between two random graph models $G^{R_1}$ and $G^{R_2}$ is defined by the distance of $G^{R_1}$ and $G^{R_2}$, where $G^{R_2}$ is a set of random graph $G^{R_2}=\{G_1^{R_2},...,G_p^{R_2}\}$ that have the same number of nodes and edges as random graph $G^{R_1}$. The distance($G^{R_1},G^{R_2}$) is obtained by comparing centralities of $G^{R_1}$ and $G^{R_2}$. Through the computational experiments, we show that it is possible to compare random graph models regardless of the number of vertices or edges of the random graphs. Also, it is possible to identify and classify the properties of the random graph models by measuring and comparing similarities between random graph models.

Fig. 1. Example RGG graph

Fig. 2. Example RRG graph

Fig. 3. Example WS graph

Fig. 4. Graphs with specific properties

Fig. 5. Centralities of graphs with specific properties

Fig. 6. Calculation of distance using centralities

Fig. 7. Flowchart for calculating distances

Fig. 8. Distances of experiment

Table 1. distance(G^PS, G^ER)

Table 2. distance(G^PS, G^BA)

Table 3. distance(G^ER, G^BA)

Table 4. Random graph model sets

Table 5. distance($G^{H}_{G}$, G^PS)

Table 6. distance($G^{H}_{G}$, G^BA)

Table 7. distance($G^{H}_{G}$, G^PS)

Table 8. distance ($G^{H}_{R}$, G^BA)

Table 9. distance ($G^{H}_{W_0}$, G^PS)

Table 10. distance ($G^{H}_{W_0}$, G^BA)

Table 11. distance ($G^{H}_{W_1}$, G^PS)

Table 12. distance ($G^{H}_{W_1}$, G^BA)

Table 13. distance ($G^{H}_{B}$, G^PS)

Table 14. distance ($G^{H}_{B}$, G^BA)

Table 15. distance ($G^{H}_{*}$, G^PS)

Table 16. distance ($G^{H}_{*}$, G^BA)