How something will spread across a network is a key question we will be interested in when analyzing many different networks, more formally we call this spreading on a network propagation or diffusion, this process of diffusion and is defined by a number of different parameters that we will be exploring in this module
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</p><p>How something spreads across a network is a key question we will be interested in asking when analyzing many different networks, the classical example of this being the diffusion of a disease through some population, but we might be talking about how the loss of one species in an ecosystem has an effect on others, the spread of financial contagion from one institution to another, or the spread of some information within a group of people. More formally we call this spreading on a network propagation or diffusion, how diffusion happens and how long it takes is defined by a number of different parameters. We will just list the primary factors involved here before looking into them individually.
</p><p>Firstly we have some infectiousness metric, where we are talking about how infectious is the phenomena that is spreading on the network.
A corollary to this is asking how resistant are the nodes to this contagion giving us a resistance parameter.
Next we need to consider the topology to the network, obviously this diffusion is taking place along the connections within the network, meaning different structures to the connections and different degree distribution will be another defining factor when considering diffusion.
Lastly we need to consider if this diffusion is taking place strategically or at random and this ties back to topology because as we have already discussed some network topologies are more susceptible to strategic influence then others.
</p><p>So Firstly to discuss infectiousness: By infectiousness we mean something that is likely to spread or influence others in a rapid manner, irrespective of the type of network it is spreading on. If you hear about some important piece of news, you feel driven to tell others and that is infectiousness, it is like an out word force that is pushing the phenomena across local connections and out over the network. We may be able to quantify this in terms of money or how contagious a disease is or a number of other metrics but we also need to ask, how many nodes a given node can infect in any given time interval? A mosquito can only bit one other creature at a time but a person can broadcast a message to possibly millions of other people at any given instance, thus enabling a much more rapid contagion rate.
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Inversely we need to think about how resistant the nodes in the network are to the spreading of this phenomena.  Imagine trying to promote gay mirage in some conservator rural community, no matter how infectious your campaign is it is unlikely to take off and this is due not to your failures but to the resistant of the other nodes in the network to this phenomena.  We could also add time to our model here, capturing how nodes may be affected for only a brief period of time before recovery, As would be the case with the spread of many diseases or some trend in fashion.
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