How are we connected? | Feat. E-think, Manon Bril & many others | EPISODE # 9
published: 11/02/21, 21:27
is this the right place to post this video?
To be precise, it should be noted that there are in reality two large families of networks: “small-worlds” characterized by groupings and short paths, and “scale-free” characterized by the presence of hubs. In practice, most networks are * both * small-world and scale-free and therefore exhibit all three properties at the same time as I describe in the video.
The mechanism which produces these graphs will be different for “scale-free” and for “small-world”. If the new points preferentially connect to the big ones, this will give a “scale-free” (and therefore hubs). To produce small-worlds, you need a preferential attachment to neighbors and some random links. For simplicity, I describe in the video a unique mechanism which produces “scale-free” and “small-world”, but they are often described separately in the scientific literature.
Finally on the law of short paths in random networks [Paul Erdös model], the length of the path between two points hardly depends on the size of the network (as indicated at 3:00), but there is however a strong dependence on the number of links that we have placed in the network. In a random network with few social links, the length of the path between two points can be relatively long.
To be precise, it should be noted that there are in reality two large families of networks: “small-worlds” characterized by groupings and short paths, and “scale-free” characterized by the presence of hubs. In practice, most networks are * both * small-world and scale-free and therefore exhibit all three properties at the same time as I describe in the video.
The mechanism which produces these graphs will be different for “scale-free” and for “small-world”. If the new points preferentially connect to the big ones, this will give a “scale-free” (and therefore hubs). To produce small-worlds, you need a preferential attachment to neighbors and some random links. For simplicity, I describe in the video a unique mechanism which produces “scale-free” and “small-world”, but they are often described separately in the scientific literature.
Finally on the law of short paths in random networks [Paul Erdös model], the length of the path between two points hardly depends on the size of the network (as indicated at 3:00), but there is however a strong dependence on the number of links that we have placed in the network. In a random network with few social links, the length of the path between two points can be relatively long.