Influence Dynamics in Social Networks

The framework of networks can be very useful when thinking about social dynamics. The people are represented as the nodes and their interactions are the connections between them. Using this model we demonstrate how someone can become influential in a social context in just a few not very obvious steps.

Project: betahaus co-working space workshops in Berlin
Objective: demonstrate how network analysis can enhance our understanding of social dynamics

When talking about social influence it may be useful to bring up the two concepts from network theory: betweenness centrality and modularity. Betweenness centrality is a measure of influence. It shows how often a node appears on the shortest path between any two random nodes in the network. In other words, a node will have a higher measure of betweenness centrality if it binds different groups together, because in order to reach from one group to another one needs to pass through that node. Modularity is an algorithm of finding communities within networks. The nodes that are more densely connected together than to the rest of the network are considered to belong to the same community. In other words, your group of friends and your family will be considered to be two different communities within your social network, because all your friends are much more likely to know each other than your family and your family members are much more likely to know each other than your friends.

To provide an example, imagine you’re hanging out at a party with the late Steve Jobs, the Google founders, and the Facebook crew. Let’s assume that you are friends with Steve Jobs who also knows your friends Larry Page and Sergey Brin from Google, but you are also friends with Mark Zuckerberg and his wife Priscilla Chan (but you don’t know Mark’s friend Sean Parker), then you are the node that has the highest influence in that network, because you bind the two groups together. The graph below shows this network and the bigger nodes are the ones that have higher betweenness centrality. The communities within the graph are shown with different colors.

Notice also how Mark has higher betweenness centrality than Sergey, Larry, or Steve, even though just like them he knows only 3 people in this network. This is because Mark brings in Sean into the group and he is the node everyone has to pass through in order to access Sean. In this way yours and Mark’s influence in the network is also showing the extent to which they experience polysingularity, as you two are the conduits between the two distinct communities that exist within.

Now take a look at what happens if Sean meets Sergey. Mark’s influence decreases, but Sergey’s influence increases. This is because Sergey now is a much better conduit between the two different communities in this network: he is in the position to provide the shortest path to Sean for the majority of people in his social circle.

What do you think Sean has to do in order to increase his influence and become more polysingular? An obvious answer would be to say, well, he should just connect to you, because you are such an influential node and if Sean is next to you, he’s binding his community to yours and thus increases his own importance.

Reality is very different, however. By connecting to you, Sean reduces both his own, Mark’s and Sergey’s influence, and only makes you more influential. This example shows that the nodes that are already well connected will increase their importance (and informational load) by integrating periphery. But the periphery doesn’t gain much influence from linking to the most connected nodes. Rather, Sean’s strategy should be different. Let’s see what happens if instead of connecting to you, he actually links up with Larry.

We now see that Sean helped Mark gain his importance again and some of Sergey’s importance went to Larry, because they both now can provide equal access through Sean to Mark Zuckerberg’s community. You are still the most influential node, because you bind the two communities together in the most efficient way.

Now if Sean wanted to raise his own influence in the network, he could actually improve his ties within his group (make a link to Priscilla). Additionally, if Sean also persuades Priscilla to cut her tie with you, then he becomes the most influential node in the network, because he binds Priscilla and Mark to your community through his links to Sergey and Larry.

That’s it: Sean took over the network and he even has the same number of links as you, Sergey or Larry. His strategy of gaining influence in the network was to first link up with the two peripheral members from another group who knew that their influence in the network will increase if they link up with Sean. The next step was to link up with someone from his own group and make them break the tie to the main node. This way Sean gained influence over network in a way that also increased the influence of 3 other peripheral members and decreased the influence of the main hub (You).