Connect-while-in-range: modelling the impact of spatial constraints on dynamic communication network structures

TL;DR

The simulation model quantifies this part of the process of network formation, realized by simply situating individuals in an environment, and provides a tool to include spatial constraints in other models of human communication, as well as dynamic models of network formation more generally.

Abstract

Like other social animals and biological systems, human groups constantly exchange information. Network models provide a way of quantifying this process by representing the pathways of information propagation between individuals. Existing approaches to studying these networks largely hypothesize network formation to be a result of cognitive biases and choices about who to connect to. Observational data suggests, however, that physical proximity plays a major role in shaping the formation of communication networks in human groups. Here we report results from a series of agent-based simulations in which agents move around at random in a bounded 2D space and connect while within communication range. Comparing the results to a non-spatial model, we show how including spatial constraints impacts our predictions of network structure: ranged networks are more clustered, with slightly higher degree, higher average shortest path length, a lower number of connected components and a higher small-world index. We find two important drivers of network structure in range-constrained dynamic networks: communication range relative to environment size, and population density. These results show that neglecting spatial constraints in models of network formation makes a difference for predicted network structures. Our simulation model quantifies this part of the process of network formation, realized by simply situating individuals in an environment. The model also provides a tool to include spatial constraints in other models of human communication, as well as dynamic models of network formation more generally.

Figures (4)

• Figure 1: Demonstration of a possible initialization and timestep in the model for $\bf{N=4, r=1, g=4.}$ Agents are randomly assigned a unique (x,y) coordinate. The coordinate space is graphically represented here as a grid(left), and agents are shown with their coordinate values. At every timestep, every agents follows the range rule: if the Euclidean distance between the agents is less than or equal to r, a link is created between them. Thus, from the initial position shown on the grid, the graph shown in the middle of the figure is formed. At the start of the next timestep, agents move at random and follow the range rule again. When previously in range agents are now out of range, the link is cut. Hence, from every agent performing random movement and following the range rule, a new network is formed.
• Figure 2: Network properties of range model (blue) and null model (red) networks for varying range between 0 and 10 (x-axes) within runs and varying population density 0.2,0.4,0.6, and 0.8 between runs (top to bottom). Dots in the graphs are time-averages of 100 timesteps, of which 100 rounds are collected at each input setting of r. Lines are drawn through the means of these time averages, and transparent areas show 1.5 standard deviations. Most visibly at low range settings (when spatial constraints are most articulated), networks are much more clustered, have slightly higher degree, higher average shortest path length, a lower number of connected components and a higher small-world index than the null model. As N varies between tests, most network measures stay the same, being predominantly influenced by r in the range model and P(connect) in the null model. At lower range settings, however, average shortest path length (and as a result, small-world index) increases noticeably with increasing N, as the disconnected groups that form at lower range settings become larger while still being highly clustered.
• Figure 3: Four sample network timesteps comparing the null model (left) to the range model (right), $N=18, g=10$. Upper left: $r=1, pc=0.1$. Lower left: $r=2,pc=0.2$. Upper right: $r=3,pc=0.3$. Lower right: $r=4, pc=0.4$.The spatial layout created by the positions of the agents in the range model graphs are copied in the null model comparisons. At similar connection probabilities, agents in the range model only connect to closer agents, creating more connected triangles.
• Figure 4: Network properties of range model (blue) and null model (red) networks for varying N between 1 and 49 (x-axes) within runs and varying r 1, 2, 3, 4, 6, 8 between runs. Dots in the graphs are time-averages of 100 timesteps, of which 100 rounds are collected at each input setting of r. Lines are drawn through the means of these time averages, and transparent areas show 1.5 standard deviations. Varying r has a clear impact on the relationship between population density and all 6 network measures, determining how densely connected graphs can become as N increases. When r approaches g, the role of agent locations diminishes until networks in the range model become like the non-spatial null model.