Part of a series on Innovation Essentials
Work in Progress Early Thoughts

I would guess you already have a gut feeling that how well innovation diffuses across a social system depends upon how well connected the social system is.

In this article I set out to answer 3 questions:

  1. Is our gut feeling correct?
  2. If so, how is diffusion affected?
  3. And, can we affect the connectivity and impact diffusion speed?

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 network manipulation to our advantage.

The Big Picture…

Innovation diffusion happens over channels in a social network. To me, that is a way of saying there is a network. So, what can the world of network topology tell us about diffusion?

Before we go reaching into the topic, let’s take a quick recap of diffusion. If you want a deeper recap, then by all means jump into my diffusion article. And when done, hit the browser’s back button to come back here.

Social systems and networks

If you recall, we use Rogers’ classic definition of diffusion. It comes from Rogers and his book “The Diffusion of Innovation“.

Diffusion is the process by which an innovation is communicated through certain channels over time among the members of a social system.

Rogers – Diffusion of Innovation

We can think of this social system as a network. It consists of a set of nodes – often people, but can be organisations. And nodes are connected to other nodes, as we see in Figure 1.

In my article on diffusion I pretended that an innovation diffused left to right through the social system in Figure 1. That allowed us to visualise an innovation entering the network on the left, to a small number of innovators, through external influences. And then internal influences diffusing it rightwards through imitators. Additionally, we could visually divide the network into Rogers’ adopter types, and so see it more as a set of interlinked social systems. And further we could discuss issues such as the chasm that exists between early adopters and early majority.

Of course, real life is not as neat as this. But it’s a useful fallacy to keep in mind to help visualise and understand the concepts.

Now it’s time to see if there is any real foundation to that masquerade! First let’s switch to using the word network instead of social system. They are the same in this case. And with that change, we will start looking at how we understand a networks shape and connections.

Network Topology

Not every network is the same. If they were, then our article would stop here as diffusion would always be the same. Rather, some networks have a lot of connections, some have a few. In some networks each node is connected to the same number of other nodes. Whereas in some networks there are a few nodes with many connections and other nodes with few. There are many shapes and structures to networks. Something we formally call a topology. And we can see some examples in Figure 2.

Figure 2: Some example social system / network topologies

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

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

Social network effects on the extent of innovation diffusion: a computer simulation. https://faculty.wharton.upenn.edu/wp-content/uploads/2012/05/social_network_effects1.pdf

Social Network Thresholds In The Diffusion Of Innovations. http://solvinnov.com/literature/social-network-thresholds-in-the-diffusion-of-innovations/

The impact of network structure on diffusion of innovation. http://solvinnov.com/literature/diffunet-the-impact-of-network-structure-on-diffusion-of-innovation/

Network model of the diffusion of innovation. http://solvinnov.com/literature/network-models-and-methods-of-studying-the-diffusion-of-innovation/

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