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Extended network flow model for Twitter

In Twitter we have the situation that the network between users is multiplex (people can hold numerous ties with each other): Users can either a) follow each other b) interact with each other or c) retweet each other. The three types of ties, manifest themselves in three different networks that can be sort of laid on top of each other. This idea got me thinking. I stumbled upon a very interesting chapter for a book from Stephen Borgatti, who introduced network flow model that in my eyes seems to fit perfectly for the Twitter network. The network model from his paper is depicted below:

Network flow model

In his model Borgatti describes the model as two kinds of phenomena, which are called backcloth and traffic in the original work of Atkin. By adapting this model for Twitter we can explain how and why the three types of ties that we have in Twitter can be laid on top of each other and how they influence information diffusion in Twitter. I have therefore made a version that shows how the concepts map onto Twitter, that is depicted below.

Extended network flow model for Twitter

The backcloth is the infrastructure that enables the traffic and the traffic consists of information flowing through the network. In the case of Twitter the backcloth corresponds to the cognitive similarities among Twitter users (see below), and to their friend and follower connections. The traffic layer consists of the interactions and flow of information that takes place on top of these phenomena.

Borgatti describes the four categories as following: “The similarities category refers to physical proximity, co-membership in social categories and sharing of behaviors, attitudes and beliefs. Generally we do not see these items as social ties, but we do often see them as increasing the probabilities of certain relations and dyadic events.” This definition corresponds to the notion of implicit ties (ties we cannot directly see) of Twitter users: These implicit ties can basically be a shared interest, a shared location, a shared demographic, a shared audience and so on. Basically every type of attribute that makes two Twitter users similar to each other. The idea that similar people with the same attributes tend to flock together is known as homophily and the general process of people forming ties with similar people is called  selection mechanism (e.g. think of people that smoke becoming friends with other smokers)

The next three types of phenomena take place on so called explicit ties because these type of ties can actually be seen or measured explicitly on Twitter. Borgatti defines the social relations category as “ the classic kinds of social ties that are ubiquitous [(which friend and follower ties are in Twitter)] and serve either as role-based or cognitive/affective ties. Role-based includes kinships and role-relations such as boss of, teacher of and friend of.[(In Twitter: follower of)] They can easily be non-symmetric [(which friend and follower ties are)].” It is apparent that, these type of ties exactly relate to the explicit follower ties, which share the same attributes and characteristics.  When we think about the other reasons why people become friends other than being similar, we  stumble upon all the network effects that are a core part of network literature. Therefore I have indicated those with the back and forth arrow above social relations. In Twitter these type of processes take place everyday: People follow prominent outlets e.g. CNN (preferential attachment), become friends with friends of friends (triadic closure) or simply follow back a person that just followed them (reciprocity). There are much more of such effects, but we don’t want to go into detail here, but instead look at the next type of ties.

Borgatti describes the interactions category as “discrete and separate events that may occur frequently but then stop, such as talking with, fighting with, or having lunch with”. This category translates into the interactional (@mention) ties in Twitter, which have exactly these behavioral traits: People do intentionally mention each other in Tweets, but also might stop doing so for certain reasons. Depending on when one looks at two users in Twitter, this interactional connection might be exist at this point in time or not. The first reason according to the network flow model, why I would interact with someone is because I follow them, which makes perfectly sense for Twitter. Now are there are more reasons why people might interact with each other and a number of those reasons is already covered in various information diffusion theories: One example is that people like to interact with others who they perceive as opinion leaders for a topic. Another example is the brokerage theory that says that such brokers tend profit from interaction with two different groups. The third type of families are the threshold models, where people believed to are lured into interaction or adoption once a certain threshold of their friends talks about a certain topic. Processes like this could easily be taking place on Twitter too.

Finally the flows category is described by Borgatti as “things such as resources, information and diseases that move from node to node. They may transfer (being only at one place at a time) and duplicate (as in information).”. This definition translates directly into the explicit retweet ties that always exist when information is transferred from one actor to another. The final network layer follows the same reasoning as the one before: The first reason why I would retweet someone is because I follow that person and I have already interacted with that person. The reasoning about information diffusion theories applies here too.

Finally I thought it would be nice to add the influence mechanism in this model, which is basically people becoming more similar to each other because of the networks that people already have. All three types of networks (friend and follower ties, @interactions and retweets) might have that effect. The classic influence example is non-smokers being friends with smokers, and then starting to smoke, might be imaginable in Twitter too. Yet there are strong indications that this effect is much smaller than people believe it to be.

Using the network flow model, we came up with a nice ordering of the different concepts that surround network science and sociology and could somehow connect this pieces to the Twitter network. I hope this extended network flow model was useful for you and hope to hear some comments on it.

Cheers
Thomas

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Great blog entry for anyone working at the intersection of social science, networks and software development.

Aurelius

Graph theory and network science are two related academic fields that have found application in numerous commercial industries. The terms ‘graph’ and ‘network’ are synonymous and one or the other is favored depending on the domain of application. A Rosetta Stone of terminology is provided below to help ground the academic terms to familiar, real-world structures.

graph network brain knowledge society circuit web
vertices nodes neurons concepts people elements pages
edges links axons relations ties wires hrefs

Graph theory is a branch of discrete mathematics concerned with proving theorems and developing algorithms for arbitrary graphs (e.g. random graphs, lattices, hierarchies). For example, can a graph with four vertices, seven edges, and structured according to the landmasses and bridges of Königsberg have its edges traversed once and only once? From such problems, the field of graph theory has developed numerous algorithms that can be applied to any graphical…

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