THE POWER OF SOCIAL NETWORKING 1

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1 THE POWER OF SOCIAL NETWORKING 1 The Power of Social Networking: Using Facebook s Open Graph data to quantify user activity on the world s largest social network Kevin A. Giardini and Matheus M. Lelis University of Massachusetts: Dartmouth MTH CSUMS May 16, 2012 Prof. Sigal Gottlieb

2 THE POWER OF SOCIAL NETWORKING 2 Abstract The goal of this research is to mathematically quantify the continuously growing activity occurring on Facebook, the world s largest social network, by developing a numerical rating system using mathematical and computer analysis. This number can then be used to systematically rank the level of user activity so as to be able to simplify individual user activity into one single numerical value.

3 THE POWER OF SOCIAL NETWORKING 3 The Power of Social Networking: Using Facebook s Open Graph data to quantify user activity on the world s largest social network The idea for this researched stemmed from a long conversation between friends about people on Facebook and how some people were out of control and how others greatly over shared information that frankly, no one wanted to know. During the conversation points were made on how certain actions were acceptable while others were frowned upon. Some time after this conversation the idea to create a rating system for all those actions, good or bad, was conceived. Background Having decided to create a rating system, the first steps were to figure out a method for actually calculating all the information. After some contemplation and research it was decided that we would base our rating system on the NFL Quarterback Rating Formula also known as Passer rating. The NFL s Passer rating formula was developed in 1971 by a special committee in order to help the NFL determine which quarterback had been the most dominant each year. The NFL s Passer Rating formula establishes a final value from values in four categories, each of these involve a separate calculation. The four categories are Completion Percentage, Average Yards Per Attempt, Percentage of Touchdown Passes, and Percentage of Interceptions. The values for all the categories are bounded so that if the result in any category is less than 0 or is greater than 2.375, the given result should be either 0 or respectively. This causes the NFL Passer Rating to have maximum possible value of The formula can be seen visually bellow.

4 THE POWER OF SOCIAL NETWORKING 4 The four separate calculations can be expressed in the following equations: ATT = Number of passing attempts COMP = Number of completions YARDS = Passing yards TD = Touchdown passes INT = Interceptions Then, the above calculations are used to complete the passer rating: Having studied and analyzed the formula we learned all we could from it and from that point it was a matter of designing our own formula for the Facebook Rating. We would use the new Graph API to tap into people s profiles and gather the data about them that was needed, once that was done we would plug in the numbers into the formula devised and from it the final rating number would be created.

5 THE POWER OF SOCIAL NETWORKING 2 The Math Set with the task of finding an equation and a framework to accurately calculate a single number to represents someone s Facebook usage, we decided to begin by looking at previous research in the field. During our research, we found a study that pieced together many different Facebook actions and how they are applied to different psychological traits, mainly, the big five: Agreeableness, neuroticism, extraversion, conscientiousness, and openness to experience. Several secondary relationships that were found in the study were the relationships between Facebook actions and shyness, loneliness, and narcissism. The study also included several tables, which outlined several different ratings they had developed for certain Facebook actions. The tables are shown below (Ryan 2011). Table 1. Means (and standard deviations) of personality characteristics among Facebook users and nonusers. Characteristic Big Five Facebook users (n = 1158) Facebook nonusers (n = 166) Extraversion 3.09 (.76) 2.80 (.73) Agreeableness 3.56 (.55) 3.51 (.55) Conscientiousness 3.36 (.55) 3.47 (.64) Neuroticism 3.04 (.76) 3.04 (.72) Openness 3.56 (.58) 3.47 (.57) Shyness Total 2.82 (.73) 2.94 (.74) Loneliness Total 3.07 (.94) 3.16 (.98) Romantic 4.50 (.93) 4.41 (.87) Family 4.43 (.59) 4.32 (.59) Social 2.80 (1.24) 3.18 (1.35) Narcissism Total (5.07) 8.85 (4.20) Exhibitionism 1.80 (1.69) 1.28 (1.35) Leadership 3.63 (2.16) 3.23 (1.94) Table 2. Factor loadings for exploratory factor analysis with varimax rotation of preferences for Facebook features. Feature ASC PE NI RTSI Status Wall Comments News feed Like Messages Photos Groups Games Fan pages Events Notes Chat Note: Factor loadings >.60 are in boldface. ASC = Active Social Contributions; PE = Passive Engagement; NI = News and Information; RTSI = Real-Time Social Interaction.

6 THE POWER OF SOCIAL NETWORKING 1 Table 3. Correlations between personality characteristics and factors of Facebook feature preference. Characteristics Big Five traits Preference of Facebook features ASC PE NI RTSI Extraversion Agreeableness Conscientiousness Neuroticism Openness Shyness Total Loneliness Total Romantic Family Social Narcissism Total Exhibitionism Leadership Note. ASC = Active Social Contributions; PE = Passive Engagement; NI = News and Information; RTSI = Real-Time Social Interaction.N = p <.05 (two-tailed). p <.01 (two-tailed). p <.001 (two-tailed). These Tables show the relationships between an individual s Facebook actions and several different personality traits. After Reading this study, we determined that we could use these weights to develop a framework where each weight contributes to an overall Facebook activity rating as well as the several different sub scores. Using these weights, we developed a series of matrix equations that determined the ratings that we were trying to determine. After developing several of the matrix equations, we put together the mathematical model. The mathematical Model consists of several different matrix equations. The first step is to determine four initial ratings: the Active Social Contribution rating (ASC), the Passive Engagement rating (PE), the News and Information rating (NI), and the Real-Time Social Interaction rating (RTSI).

7 THE POWER OF SOCIAL NETWORKING 2 [ ASC ] = [ ] [ PE ] = [ ] [ NI ] = [ ] (5000 / 250) min(# Statuses,250) (5000 / 250) min(# WallPosts,250) (5000 /100) min(# Likes,100) (5000 / 200) min(# Messages,200) (5000 /1000) min(# Photos,1000) (5000 / 25) min(# Groups,25) (5000 /10) min(# Games,10) (5000 /15) min(# Events,15) (5000 /10) min(# Notes,10) (5000 / 250) min(# Statuses,250) (5000 / 250) min(# WallPosts,250) (5000 /100) min(# Likes,100) (5000 / 200) min(# Messages,200) (5000 /1000) min(# Photos,1000) (5000 / 25) min(# Groups,25) (5000 /10) min(# Games,10) (5000 /15) min(# Events,15) (5000 /10) min(# Notes,10) (5000 / 250) min(# Statuses,250) (5000 / 250) min(# WallPosts,250) (5000 /100) min(# Likes,100) (5000 / 200) min(# Messages,200) (5000 /1000) min(# Photos,1000) (5000 / 25) min(# Groups,25) (5000 /10) min(# Games,10) (5000 /15) min(# Events,15) (5000 /10) min(# Notes,10)

8 THE POWER OF SOCIAL NETWORKING 3 [ RTSI ] = [ ] (5000 / 250) min(# Statuses,250) (5000 / 250) min(# WallPosts,250) (5000 /100) min(# Likes,100) (5000 / 200) min(# Messages,200) (5000 /1000) min(# Photos,1000) (5000 / 25) min(# Groups,25) ASC = Active Social Contribution Rating PE = Passive Engagement Rating NI = News and Information Rating RTSI = Real-Time Social Interaction Rating (5000 /10) min(# Games,10) (5000 /15) min(# Events,15) (5000 /10) min(# Notes,10) In these four matrix equations, we included a matrix that contains the amount of several different Facebook Actions: status updates, wall posts, likes, messages (outbox), photos, groups, games, events, and notes. Using the Facebook s Open Graph data, we are able to see up to 5,000 occurrences of each action. Collaborating on the research, we decided that some of the actions were unlikely to get up to 5,000 occurrences. Therefore, we decided to include a maximum value for each action and scale them up to a level of 5,000 (as seen by the min function being multiplied by 5000 divided by a certain number to get the number of Facebook actions out of 5000). The weights in these four matrix equations represent how much each Facebook action matters to the final rating. For example, the Passive Engagement rating (PE) is affected the most by the amount Facebook groups an individual is a member of, while the Real-Time Social Interaction rating (RTSI) is affected the most by the number of outgoing messages an individual has. Next, the ratings from the four previous matrix equations are entered into two more equations to determine 8 different activity ratings: the big five as well as shyness, loneliness, and

9 THE POWER OF SOCIAL NETWORKING 4 narcissism. The ratings from the last four calculations are entered in as their own matrix and multiplied by another matrix which includes different weights that show how much each rating matters to the big five and the other three ratings. For example, a high level of Extraversion will be caused by a high Active Social Contribution rating (ASC) and a high level of loneliness will be caused by a high Passive Engagement rating (PE) [ ASC PE NI RTSI] = [ AG CO EX NE OP] AG = Agreeableness Rating CO = Conscientiousness Rating EX = Extraversion Rating NE = Neuroticism Rating OP = Openness to Experience Rating [ ASC PE NI RTSI ] = [ SHY LON NAR] SHY = Shyness Rating NAR = Narcissism Rating LON = Loneliness Rating Finally, the eight different sub scores are then added together to find a single value, which represents the level of an individual s Facebook activity. Applications The point of this equation is not to simply compare one person against another and try to see who s better at Facebook. This formula can actually be used for marketing purposes to allow businesses to better target their customers. For example a Paintball field would better invest it s money if it tried to advertise to someone who had a higher OP rating than someone

10 THE POWER OF SOCIAL NETWORKING 5 who would rather stay inside. By looking at the individual sub scores a marketing agent could more accurately target his ads. On top of that, a psychiatrist could also use these sub scores to better understand his patients, allowing him to better treat them. This being possible since the scores are based on psychological aspects of a person.

11 THE POWER OF SOCIAL NETWORKING 6 References Who uses Facebook? An investigation into the relationship between the Big Five, shyness, narcissism, loneliness, and Facebook usage, by Tracii Ryan and Sophia Xenos, Computers in Human Behavior, Vol. 27, No. 5. (08 September 2011), pp NFL Quarterback Rating Formula. QB Rating Calc. May 12, 2012