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Comparison of two types of Influencer’s impacts on a cascade

In the pre-internet time, people belonged to each cluster.

Each cluster had a high density, each cluster was separated, or was connected to another cluster by weak bond due to restrictions; those included geographical factors (e.g., people were living far from each other, and only people knew people within that community), social factors (e.g., there is no need to other people from other community), etc.

In this situation, it wasn’t easy to have some new things spread through the network.

The development of influencers makes it faster to spread new things. The reading https://influencermarketinghub.com/what-is-an-influencer/ mentioned the types of influencers, including macro-influencers, micro-influencers, and nano-influencers, which differ from the number of followers and impacts, and other things related to media, including different platforms. I would like to focus on the impact of influencers, and how different numbers of followers could make changes differently.

 

Compare the situation without and with an influencer:

1. Nano-influencers are people with “a small number of followers,” according to the reading. If I were to make it more extreme, we could choose a node in the existing cluster as the first adopter, with no extra edges being added. For example, in a community, choose the person with the most friends be the first one to use a new thing. 

When not having an influencer, the network might look like this:

                   

In this graph, there are nodes with 1, 2, and 3 friends, respectively. Consider the threshold p to switch from blue to red is ½.

To spread something, we choose the node that has the highest number of friends, which is 3, and those nodes are nodes C, E, and F.

1.1 Choose Node C

  

1.2 Choose Node E

   

1.3 Choose Node F

  

We notice that though having the same number of friends, only node C could make it spread through the whole network. The difference between node C and node E & F is the next level of nodes of the node that it connects to. Nodes E and F connect to node G, which does not have enough power to keep spreading it. Therefore, it means that being a good influencer is not only about reaching out to a certain amount of people, but it is also about choosing the right people to spread to.

2. Macro-influencer in the reading was another type, who has a huge number of followers, it increases the chance that the network got spread through. Example: A company selects a person and makes it appear on many social media, so that everyone knows this person.

In the lecture about networks, we talked about how weak ties and strong ties are, and I consider the connections between users of social media and influencers as weak ties. Slightly different from the weak ties mentioned in class, these connections are powerful weak ties:

  1. such connection has direction, and so does the direction of spread – whether a user uses something has no impact on the influencer’s choice, but it works in the other direction.
  2. such weak ties are coming out of the influencer and have a huge amount, some are even as high as millions. However, the nodes that it connects to (users) are not likely to see those influencers in person.

If I add those two factors to a normal network (high number & directional connection), the illustration would be like this:

  

In this way, everyone in this network would end up being influenced. It is because that the adoption of the new things of this influencer increases for sure the ratio of people who adopts it that each node connects to. In the first round, though node F still does not adopt it, node A being ¼ of the nodes that F connects to is using it, which could have been 0. Such an increase in the ratio finally has some effects in the later round.

 

Other findings:

  1. In addition, since it is directional, having an influencer might sometimes negatively affect the spread of people who adopt it. For example, in the graph below, if we have node E be the first adopter, in section 1.2, we could have ended up having nodes B, E, and G all adopt it. However, node A won’t adopt it because of E’s choice because only A (the influencer) could affect E. Also, since the existence of influencer increases the number of connections that each node has, the fact that the A is not using it decreases the ratio of connections that use it from ½ (in section 1.2) to 1/3 (in this case), and it prevents G from adopting it.

  

2. The fewer friends that this person has, the easier that this person would follow the influencer.

In all cases mentioned above, node B was always the first one who adopt it, as long as one of its friends adopts it. In reality, if a person has few friends, he would have fewer people as a reference. A small increase in the number of his friends using it would greatly increase the ratio, making it more advantageous and generating more incentive for him to change.

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