Innovation: Diffusion, and What Network Topology can tell us

 Under Dev Preliminary
Please note: this article is under development - it may change (improve ) between visits
Please note: this article is just preliminary thoughts at the moment and needs some work

You probably already have a sense that how a social system is connected alters the way, and speed, an innovation could diffuse.

Welcome to the world of network topology. It offers the promise to discover influencers, groups of loosely connected adopter types, mavens, potential problem areas and more.

Key take-aways

  • Point 1

Network Topology

Does a network with many connections diffuse innovations quicker than one with few connections? Well, it depends on the shape and structure of the network. Something we formally call a topology, and you can see some examples in Figure 2.

Figure 2: Some example social system / network topologies (non-animated)

If we can understand the social system’s topology, we get some insights into how to diffusion is likely to work, where it might stall, and how to increase our odds. Network topology, whilst we can visualise in a diagram, is more commonly captured by describing a set of attributes the network has.

Network attributes

These topologies are shorthand for a set of attributes that we can measure about the network. Such as those in Figure 3.

Figure 3: Some example network metrics (non-animated)

We could write article after article on network topologies and metrics. You can find some descriptions in this Wikipedia article.

What do attributes tell us about Diffusion?

And these: https://pdfs.semanticscholar.org/00b5/c5a40fa07938bd74091257591bce87f9bc2c.pdf

Let’s consider some examples

Density and diffusion success probability

The less dense a social system is, the more likely diffusion will fail.

Think of a network of 100 people. Let’s say everyone is connected to everyone. Here the density would be 99/99, or 100%. There’s lots of redundant channels for diffusion to travel over.

But what if each person can only talk to at most 2 neighbors? Well, each person could still potentially talk to 99 others, but can practically only talk to at most 2. This has a very low density: 2/99 or 2%. It just takes one person to refuse to diffuse and division stops

Weak ties – crossing group boundaries

Several groups of people, each group sharing some an attribute that is different. However, the are some people in each group connected loosely to some in the next group. This is better for diffusion than the first example. But, if those connecting people don’t diffuse then we might observe a chasm preventing diffusion.

Structural holes – carrying innovation

IT consultancies (should) act as organisations with weak ties, bridging holes. By this I mean that they are active in many different industries and markets. And so, they have a great opportunity to “carry” innovations from one to another.

Eigenvectors and Mavens

Eigenvectors can help us understand the importance of a node – Google used them in the initial page rank algorithm. This might help us find the Mavens that Gladwell talks of in The Tipping Point.

Degrees of centrality and social influencers

if we can identify a person with a very high out-degree of centrality (i.e. connected to a lot of people) we might have found a “social influencer”

Finding a networks topology

It sounds great, right? Finding a networks topology means we can find the influencers, the weak points, and work out how to accelerate diffusion. Sadly, in practice it can be a little harder.

What if we are looking at an organisation? We could believe that the hierarchical organisation chart is the social system. However, if we look at who regularly talks to who, a different social system would emerge. And it is that second social system that usually affects diffusion. We can run surveys to discover this. Or even analyse communication tools the organisation uses, such as email threads.

Outside an organisation is a little more difficult. People in general are less likely to answer surveys and we can’t monitor communications. However, social networks, such as LinkedIn and Facebook, offer a little hope of understanding some networks better.

https://en.m.wikipedia.org/wiki/Social_network_analysis_software

It is now clear that different types of network structures yield predictable differences in aggregate diffusion curves (Dover, Goldenberg and Shapira, 2012, Trusov, Rand and Joshi, 2013).” https://www.researchgate.net/profile/Gary_Russell2/publication/317168743_A_New_Bass_Model_Utilizing_Social_Network_Data/links/592841b60f7e9b9979a3571f/A-New-Bass-Model-Utilizing-Social-Network-Data.pdf?origin=publication_detail

calibration of the classical Bass model on sparsely-connected social networks results in biased estimates of diffusion parameters: social influence (q) in the Bass model is biased downward, while external influence (p) is biased upward. In contrast, we show that the diffusion parameters of the NBB model are accurate regardless of the network structure. Moreover, the NBB provides superior fit compared to the traditional Bass model. https://www.researchgate.net/profile/Gary_Russell2/publication/317168743_A_New_Bass_Model_Utilizing_Social_Network_Data/links/592841b60f7e9b9979a3571f/A-New-Bass-Model-Utilizing-Social-Network-Data.pdf?origin=publication_detail

https://www.sciencedirect.com/science/article/pii/S0167811618300284
The effect of social networks structure on innovation performance: A review and directions for research

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