Statistical Analysis of the Properties of Geometric Network with Node Mobility

TL;DR

The paper investigates how mobility alters the geometry and connectivity of random geometric networks. It extends static random geometric graphs to Geometric Networks with Mobile Nodes (GNMN), where a subset of nodes move according to Brownian motion with rest periods and update connections as positions change. It provides analytic approximations for key metrics such as $P(nei)$, $E[nei]$, $P(sec\_nei)$, and $E[CB(i)]$, and conducts extensive simulations to characterize how radius $r$, velocity $v$, and rest time $t\_rest$ affect degree distributions, second-hop neighborhoods, centrality, and connected components. The results show that increasing $r$ densifies the network and that higher $v$ and $t\_rest$ introduce more dynamism and connectivity fluctuations, with centrality rising with radius and a potential application to epidemic spreading and information propagation in mobile wireless and social networks.

Abstract

The movement changes the underlying spatial representation of the participated mobile objects or nodes. In real world scenario, such mobile nodes can be part of any biological network, transportation network, social network, human interaction, etc. The change in the geometry leads to the change in various desirable properties of real-world networks especially in human interaction networks. In real life, human movement is concerned for better lifestyle where they form their new connections due to the geographical changes. Therefore, in this paper, we design a model for geometric networks with mobile nodes (GNMN) and conduct a comprehensive statistical analysis of their properties. We analyze the effect of node mobility by evaluating key network metrics such as connectivity, node degree distribution, second hop neighbors, and centrality measures. Through extensive simulations, we observe significant variations in the behavior of geometric networks with mobile nodes.

Figures (5)

• Figure 1: The random geometric network is formed considering varying radius (a) - (c), velocities (d) - (f), and $t_{rest}$ (g) - (i).
• Figure 2: Trend of second hop neighbors based on the value of varying radius, velocity and $t_{rest}$
• Figure 3: Degree distribution of the nodes in the random geometric graph plotted for different values of radius, velocity, and $t_{rest}$
• Figure 4: Average centrality measures; degree, and betweenness for different values of radius, velocity and $t_{rest}$.
• Figure 5: Random geometric network having different number of connected components for varying radius, velocity and $t_{rest}$.