Modeling Spatial Social Complex Networks for Dynamical Processes

Figure 1

Growth rules for the baseline (a) and the revised SSCN model (b & c). (a) A new node joins the network and connects directly to a randomly selected node , with probability , settling away from according to the rule of (2) (left panel). With probability the connection is redirected to a random neighbor of and settles at distance from (right panel). (b) Befriending closest neighbors (shown for ). Left panel: Node needs to add a connection to the nearby node on its left, in order to fulfill the requirement of connections to at least nearest neighbors. The new link and ’s 2 nearest friends are highlighted in green. Right: The process is repeated for all nodes in the network until all fulfill the minimum- requirement. The new links added to the baseline model are highlighted in green. (c) Relocation of node happens in two stages. Left: In the first stage is translated to within distance 1 from a randomly selected node . All of ’s old contacts (broken orange lines) are retained (orange lines). Right: In the second stage links are added to ensure connection to at least new closest neighbors of (shown for ). A new link and the 2 closest neighbors are highlighted in green. Note that relocation does not alter the connectivity pattern in step 1, but the relocating node may acquire up to new links in step 2.

(a) Baseline SSCN: redirection mechanism and spatial location

(b) Connecting to spatially closest neighbors

(c) Relocation of a node