Thursday, September 10, 2009

Measuring Influence

With word-of-mouth being the most trusted and valuable source of information, influence then plays a huge role in how we connect. But what is influence and how do we measure it? This is where the worlds of sociology, discrete mathematics, and marketing begin to collide, three of my most favorite subjects!

The study of influence is a “fundamental property of social structures” (Hanneman, 2005) in sociology; however, determining exactly what influence is and how to describe it is not so fundamental. To look at influence, one first must consider the social network which is “a map of all of the relevant ties between all the nodes being studied.” (Wiki-social network) Social network analysis studies the relationships and connections of the people in a network; therefore, network theory and graph theory can be used to begin to understand how to measure influence.

I will not even attempt to fully describe social network analysis, network theory and graph theory in this setting, nor would I be able to do it justice. So my goal is to get you thinking about the different ways influence can be viewed and some of the high level tactics of measuring those perspectives.

Note: I will refer to nodes or vertices as people and edges or paths as connections or relationships.

There are many different approaches to measuring influence and each depends on the particular calculation and the structure of the network. At the core is centrality. Centrality measures a “rough indication of the social power of a node (person) based on how well they "connect" the network.” (Wiki-social network analysis) It tries to describe how close a person is to the “center” of the action in the network. "Degree", "Betweenness", and "Closeness" are all measures of centrality.

Degree is the count of the number of relationships to other people in the network. This is also known as the geodesic distance. Simply stated, degree is the number of friends a person has or the number of followers a person has. However, which is more influential, a person with a high degree or a person with a low degree, but high connectivity? For instance, Person A has direct connections with 10 other people and Person B has potential to influence 15 people through the indirect connections that he has with his 4 direct connections.

Betweeness is the number of people who a person is connecting with indirectly through their direct relationships. Let’s suppose I’m looking for a job and a friend’s mother knows the hiring manager. I need to make contact with the hiring manager, but since I don’t know him personally I need to connect to him through my friend who connects through her mother. The people (my friend and her mother) who lie “between” me and the hiring manager have the influence. The betweeness centrality is higher when the person falls on the geodesic paths between other pairs of people in a network. In other words, the more people that depend on Person A to make connections with other people the more influence that Person A has.

Closeness is the degree a person is near all other persons in a network (directly or indirectly). It reflects the ability to access information through the "grapevine" of network members. (Wiki-social network analysis) People that have short geodesic distances to other people within the graph have higher closeness. Influence “comes from acting as a “reference point” by which others judge themselves, and by being a center of attention whose views are heard by a large number of people.” (Hanneman, 2005) In the most basic sense, closeness is shortest-path length. People who are able to reach other people at shorter path lengths or who are more reachable by other people at shorter path lengths have more influence. Another way to think about closeness is reach.

Eigenvector centrality “is a measure of the importance of a node in a network. It assigns relative scores to all nodes in the network based on the principle that connections to nodes having a high score contribute more to the score of the node in question.” (Wiki-social network analysis) Using eigenvector centrality you can attempt to measure indirect influence. “A person’s influence is proportional to the total influence of the people to whom he is connected.” (Farmer, 2007)

Now that we’ve described the main terms related to measuring influence let’s switch gears and take a look at two tools that are trying to measure influence in regards to Twitter, Twitalyzer and Klout.

Twitalyzer measures “Influence”, “Signal”, “Generosity”, “Velocity” and “Clout.” According to the website the Influence calculation is based on the following:

  • Your relative reach in Twitter, measured by the number of followers you have
  • Your relative authority, measured by the number of times you are "retweeted"
  • Your relative generosity, measured by the number of times you "retweet" others
  • Your relative clout, measured by the number of times you are referenced by others
  • Your relative velocity, measured by the number of updates you publish over a seven day period

Klout measures influence by looking at the user's social graph. They calculate the size of a person’s audience by determining the “True Reach.” True Reach considers how active a user's network of followers actually is, as well as, how engaged a person's followers are. This calculation takes into account more than just follower count to determine the size of someone’s audience. Next, Klout analyzes the size and strength of a person’s likelihood that someone will listen or act upon any specific message by looking at interactions across the social graph. Then they use +25 variables to answers 6 types of questions:

· Engagement

o How diverse is the group that @ messages you?

o Are you broadcasting or participating in conversation?

· Reach

o Are your tweets interesting and informative enough to build an audience?

o Do a lot of people retweet you or is it always the same few followers?

· Velocity

o How likely are you to be retweeted?

o Do a lot of people retweet you or is it always the same few followers?

· Demand

o How many people did you have to follow to build your count of followers?

o Are your follows often reciprocated?

· Network Strength

o How influential are the people who @ message you?

o How influential are the people that retweet you?

· Activity

o Are you tweeting too little or too much for your audience?

o Are your tweets effective in generating new followers, retweets and @ replies?

The variables are normalized across the whole data set and run through an analytics engine. After the first pass of analytics Klout applies a specific weight to each data point. Then the factors are run through machine-learning analysis and the final Klout Score is calculated showing a value for an individual’s influence.

Klout goes a step further for businesses and also provides insight into who you want to be talking to about your brand and spreading the word about your product allowing Klout to calculate topic-specific scores. And finally they help you understand who the user actually influences by measuring the strength of influence between every relationship on a user’s social graph. (Measuring Twitter Influence)

Twitalyzer takes a simple and straight forward approach to calculating influence whereas Klout bases its calculation on a more complex approach. Since Klout doesn’t reveal their algorithms we can only assume that they use a variety of methods that we have discussed above to calculate influence.

This review is not exhaustive nor does it attempt to dive into the depths of linear algebra and graph theory that serve as the backend, but it illustrates that there are many ways to calculate influence. In addition, this post shows how the art and science of marketing, mathematics, and sociology come together in order to fully understand the dynamics of influence. Within each of the above concepts there are multiple algorithms to compute a value to represent influence. It’s important that we are aware of this so that when we discuss PageRank, Facebook’s newsfeed, Twitter influence, etc. we understand what data the “visualization” is showing us and that on the backend there is a calculation that is being done to assign a value to where someone lies in the social graph. This social graph is key for marketers to maximize exposure to their products.


Farmer, J. (2007, November 2). Graph Theory: Part III (Facebook). Retrieved from 20bits by Jesse Farmer:

Hanneman, R. A. (2005). Introduction to social network methods. Retrieved from

Measuring Twitter Influence. (n.d.). Retrieved from Klout:

Wiki-social network. (n.d.). Retrieved from Wikipedia:

Wiki-social network analysis. (n.d.). Retrieved from Wikipedia:


  1. Leigh Anne, Great post on quantifying influence. I sense a follow-up post comparing some of the metrics and a few of the platforms. For a different perspective on Influence, take a look at the WOMMA's Influencer Handbook,

  2. Leigh Anne, Nice post. But isn't there a difference between the influence of a individual (node) and the centrality measures, which characterize the structure of the network?

  3. @warren thanks for the tip on the WOMMA perspective, I will take look.

    @peter interesting question. I see it that you can't have one without the other. There's no influence of the individual (node) without the network, so you have to look at how the individual is influencing the rest of the network. And you have to look at how the network is "affected" by the individual. Maybe I'm not understanding your question. I'm interested to hear your thoughts.