Networked life

We are all susceptible to the pull of viral ideas. Like mass hysteria. Or a tune that gets into your head that you keep on humming all day until you spread it to someone else. Jokes. Urban legends. Crackpot religions. No matter how smart we get, there is always this deep irrational part that makes us potential hosts for self-replicating information.”   Snow Crash (1992)

For those of you interested by Networks and Networked life, here are three mathematical models explaining visually some of the key concepts behind “virality/contagion” in networks. A truely fascinating experience !

Simulation 1 – Forest Fire: this graphical simulation models the propagation of a forest fire in a woody area. To proceed, set the probability for each square to contain trees to a low value (i.e. 0.1). Click on: (1) “Forest” to draw the map, (2F “fire” to ignite, and press start to observe the propagation of the fire. Repeat the experience by raising gradually the probability from 0.1 up to 0.7. Something unexpected happens for p values comprised between 0.4 – 0.6. 

Simulation 2 – Viral infection: same as before, but modelling the pread of viral infection among susceptible hosts. To start-up with, fix the parameters to: number of nodes = 200, average node degree = 1, initial outbreak size = 1, virus spread chance = 10%, and all the remaining three bars at their minimum. Click on Set-up and then Go. repeat the experience raising the average-node-degree one by one. This parameter describing intrinsic connectivity is key for the appearance of massive and explosive contagion.

Simulation 3Self-assembly of a network using the Erdös-Renyi model: the model matches unrelated pairs of nodes. Once the average number of connections per node overcomes 1, something dramatic appears…Set the parameters to: number of nodes 300. The simulation higlights that formation of giant networks occur spontaneously, as an intrinsic property of the system. Avalanche/viral reponse occurs when the average number of connections per node slightly overcome 1. These “Thresholds” are fundamental characteristics of virality in social networks.

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