Hello. You say that many real world phenomena are modelled well by this small-worldness. I have been trying to use small worldness measures sigma (Humphries et al., 2008); Omega (Telesford et al., 2011) and phi (Muldoon et al.,, 2016) for real world phenomenons but find problems (e.g., they are largely correlated to average connectivity weights despite normalisation; different SW measures suggest different things etc., ). In principle the model is striking, however measurement is not simple. Does anybody have any suggestions or advice regarding this?
It, therefore, appears that social media as well the web would both exhibit both small world (distributed) characteristics and Scale-free (centralized) characteristics? Not really clear.
Yeah, it's kind of confusing, but I don't think the two are mutually exclusive. You can have a centralized graph where most vertices aren't neighbors yet still reach other quickly through the central nodes/hubs, or you could have a decentralized graph with many local hubs and a few global connections that accomplishes the same small-world characteristics. I think both scale-free and decentralized can be small-world. Hope this helps.
I don't see the difference, both are defined as networks with local clusters that connect with each other right? High clustering coefficient and low average shortest path.
Akis Linardos I think it’s because the ‘small world’ property is also true of scale free networks, but scale free networks are not the same as decentralised networks
@Matt Lowe I like your explanation. I suppose in a fully centralized graph every vertex can be reached from every other one in just 2 steps, even though they're not neighbors, so you can have a centralized small world network.
Thanks for the video.
Hello. You say that many real world phenomena are modelled well by this small-worldness. I have been trying to use small worldness measures sigma (Humphries et al., 2008); Omega (Telesford et al., 2011) and phi (Muldoon et al.,, 2016) for real world phenomenons but find problems (e.g., they are largely correlated to average connectivity weights despite normalisation; different SW measures suggest different things etc., ). In principle the model is striking, however measurement is not simple. Does anybody have any suggestions or advice regarding this?
It, therefore, appears that social media as well the web would both exhibit both small world (distributed) characteristics and Scale-free (centralized) characteristics? Not really clear.
Yeah, it's kind of confusing, but I don't think the two are mutually exclusive. You can have a centralized graph where most vertices aren't neighbors yet still reach other quickly through the central nodes/hubs, or you could have a decentralized graph with many local hubs and a few global connections that accomplishes the same small-world characteristics. I think both scale-free and decentralized can be small-world. Hope this helps.
well explained. frankfurt is further down south though if may remark this
so Decentralized and Small World Networks are basically the same thing?
Not really, they are similar but they are defined differently, best not mix the terms as they mean different things
I don't see the difference, both are defined as networks with local clusters that connect with each other right? High clustering coefficient and low average shortest path.
Akis Linardos I think it’s because the ‘small world’ property is also true of scale free networks, but scale free networks are not the same as decentralised networks
@Matt Lowe I like your explanation. I suppose in a fully centralized graph every vertex can be reached from every other one in just 2 steps, even though they're not neighbors, so you can have a centralized small world network.