How many random links does it take before most people are in one connected cluster? While mean-degree is below 1, floods stop after a few cyan people and the bright links stay local.
Try this Set edges-per-tick to 1 and press Reset to start with no links (the setting itself takes effect live). Links now arrive at about 0.8 per tick, so the jump between mean-degree 1 and 2 is spread over roughly ticks 50 to 110 and is easier to follow in the Giant component graph.
About this model Where it ends up
The giant component of Erdős and Rényi's random graphs (1960), the subject of Uri Wilensky's Giant Component in the NetLogo Models Library. As random links are added, the largest connected cluster stays small until the average degree reaches 1, then quickly takes in most nodes. Everyone is connected once the average degree passes about ln n.
People sit evenly spaced on a ring; their number is nodes, read only at setup. Each tick, each person starts a link to a random other person with probability edges-per-tick / nodes, rounded down to a whole percent, so at the defaults about 1.6 links are added per tick rather than 2. Person 0 starts wet (cyan), and each tick dry people linked to a wet person get wet, one hop at a time; links between wet people turn bright. When the wet count has not changed for reseed-every ticks, everyone dries and each person becomes a new seed with probability 1/nodes, so a reseed can start zero, one or several floods. edges-per-tick and reseed-every are read every tick.
component-now is the current wet count, peak-component-size its maximum so far, and covered-fraction the wet percentage. edge-count and mean-degree count link attempts, including repeats of an existing link. NetLogo's version finds the largest component directly each tick; here component-now is whatever the current flood has reached, which is the largest component only if the seed landed in it. The run never stops by itself.
