Chapter 5. Identification of Factors Impacting Individuals’ Interactions
5.2. Experimental Results
5.2.1. How Network Visibility and Strategic Networking Leads to the
5.2.1.2. Experimental Results
In this part of our experiments we have two sets of experiments (i.e., Figure 5.4 and Figure 5.5) each of which contains three different configurations (with respect to different underlying network structures and methods and strategic responses towards the process of network growth with different network visibility). In particular, these figures
102 show how changes in the main characteristics of the network occur with respect to different parameter configurations. The process of network growth continued until the size of the network reached 200 (N = 200). The x-axis shows the simulation periods while the y-axis shows network characteristics (i.e., Clustering coefficient and Average path length).
Plot legends show the variability in parameter K. In Figure 5.4, we plotted average path length (AVL) of the networked individuals with respect to different underlying network structures and in the presence of one strategic response upon the process of network growth. The x-axis shows the simulation periods while the y-axis shows Average path length of the network. As we can see regardless of underlying network structure, when the network visibility is set to a small number (i.e., k =2) the average path length of the network appears with bigger values. The maximum values of AVL in figure 5.4(A), 5.4(B) and 5.4(C) range from 9 to 13. When k = 2 individuals are only able to search for the possible candidates (that link establishment with them provide them the highest utilities) only two hops away from themselves. And it reduces the chance of meeting other possible candidates from other parts of the network. Another observation from these series of pictures is that when the visibility of the individuals is set to higher values (i.e., k =10) we are able to observe a huge shrink in the network average path length. The minimum values of AVL in figure 5.4(A), 5.4(B) and 5.4(C) range from 3 to 5. This shows that visibility of the nodes towards the global topology of the network will provide them a better chance to select the best candidates from all position of the network in the utility maximization process. Having said that the smallest AVL belongs to the network which its underlying network structure has been set to Random Network. The resulting network with the AVL of three is generated when K= 10.
103 A
B
C
Figure 5.4 : Average path length of the networked individuals with respect to different underlying network structures and in the presence of one strategic response upon the process of network growth. The x-axis shows the simulation periods while the y-axis shows networks’ Average path lengths). Plot legends show the variability in the visibility parameter K.
104 We also tested a new scenario in which the method of network growth triggers strategic responses for all direct neighbors. An interesting observation is that there is no large gap among the AVL values with respect to visibility parameter k in this case.
Although still when the visibility is set to higher values the AVL values are smaller but the differences are not really significant. This shows that strategic responses of all direct neighbors help the whole population to reach each other in shorter steps and consequently it reduces the impact of visibility parameter K.
In detail, one can see that average path length of the network is the highest when the method of network growth is set to Strategic Growth. That is to say, new individuals enter the networks in a way to maximize their utilities so they search for the best candidate among the existing network members to provide them the highest utility (based on the co- author formulation the one who has the lowest degree of connectivity). As we observed calculated AVL values in figure 5.4 were quite large. This indicate the fact that utility maximization process of the individuals lead to a network with higher average path length which consequently make the individuals to be far from each other. It can easily be observed that, as long as a large population of individuals adopt such strategic responses, we can expect decrease in the network average path length.
105 A
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Figure 5.5: Clustering Coefficient of the networked individuals with respect to different underlying network structure and in the presence of one strategic response upon the process of network growth.
The x-axis shows the simulation periods while the y-axis shows networks’ Clustering coefficients.
Plot legends show the variability in visibility parameter K.
106 We repeat the same set of experiments, however this time we calculated the emerging Clustering Coefficient (CC) of the networks. The result of our experiments are depicted in Figure 5.5. In particular, these figures show how changes in the clustering coefficient of the network occur with respect to different parameter configurations. The x-axis shows the simulation periods while the y-axis shows clustering coefficient of the network. As we can see regardless of underlying network structure, when the network visibility is set to a small number (i.e., k =2) CC values appear to be larger. However, when the visibility of the individuals is set to higher values (i.e., k =10) it leads to a huge change in the Network’s clustering coefficient. This shows that better visibility of the nodes towards the global topology of the network does not lead to a network with higher clustering coefficient among its members. This indicates the fact that lower visibility towards global topology of the network leads to emergence of having network structures with higher clustering coefficient among its members.