THE POWER OF SOCIAL NETWORKING 1

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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 499
-

CSUMS

May 16, 2012

Prof. Sigal Gottlieb




THE POWER OF SOCIAL
NETWORKING


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Abstract



The goal of this research is t
o mathematically quantify the continuou
sly 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.

THE POWER OF SOCIAL
NETWORKING


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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 poi
nts 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 syste
m, 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 N
FL’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, eac
h 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 i
f the result in any

category is less than 0

or
is greater than
2.375, the given result should be
either
0

or

2.375

respectively
. This
causes

the
NFL Passer
Rating to have

maximum possible
value of
158.3.
The formula can be seen visually bellow.



THE POWER OF SOCIAL
NETWORKING


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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 th
at 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.


THE POWER OF SOCIAL
NETWORKING


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The Math


Set with the task of finding an equation and a framework to accurately calculate a single
number to re
presents 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, main
ly, 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

Facebook
users
(
n

=

1158)

Facebook
nonusers
(
n

=

166)

Big Five

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

10.28 (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

.81

.09

.08

−.07

Wall

.77

.09

.12

.09

Comments

.76

.23

.07

.06

News feed

.68

.17

.03

.03

Like

.67

.33

.07

.09

Messages

.61

.00

.13

.41

Photos

.60

−.17

.37

.09

Groups

.18

.71

.25

.16

Games

.05

.70

−.08

−.03

Fan pages

.20

.69

.25

.10

Events

.15

.11

.75

.03

Notes

.07

.14

.72

.05

Chat

.08

.14

.06

.93


Note
: Factor loadings >.60 are in boldface. ASC

=

Active
Social Contributions; PE

=

Passive Engagement;
NI

=

News and Information; RTSI

=

Real
-
Time Social
Interaction.




THE POWER OF SOCIAL
NETWORKING

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Table 3.

Correlations between personality characteristics and factors of Facebook feature preference.


Characteristics

Preference of Facebook features



ASC

PE

NI

RTSI

Big Five traits

Extraversion

.14
⁎⁎⁎

−.12
⁎⁎⁎

.01

.11
⁎⁎⁎

Agreeableness

.06


.02

.06


.05

Conscientiousness

.03

−.05

−.08
⁎⁎

.05

Neuroticism

.08
⁎⁎

.10
⁎⁎⁎

−.04

−.05

Openness

−.05

.01

.11
⁎⁎⁎

−.02


Shyness

Total

−.05

.11
⁎⁎⁎

−.04

−.08
⁎⁎


Loneliness

Total

−.09
⁎⁎

.10
⁎⁎⁎

.01

−.02

Romantic

.04

−.06

−.01

.03

Family

.04

−.01

.08
⁎⁎

.08
⁎⁎

Social

−.10
⁎⁎

.09
⁎⁎

−.09
⁎⁎

−.04


Narcissism

Total

.06


−.10
⁎⁎

.06

.04

Exhibitionism

.09
⁎⁎

−.04

.12
⁎⁎⁎

.06


Leadership

.01

−.08
⁎⁎

.04

.04


Note.

ASC

=

Active Social Contrib
utions; PE

=

Passive Engagement; NI

=

News and Information; RTSI

=

Real
-
Time
Social Interaction.
N

=

1158.

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 overal
l 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 to
gether 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 Infor
mation rating (NI), and the Real
-
Time Social
Interaction rating (RTSI).


THE POWER OF SOCIAL
NETWORKING


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THE POWER OF SOCIAL
NETWORKING


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ASC


= Active Social Contribution Rating







PE




= Passive Engagement Rating


NI




= News and Information Rating

RTSI

=

Real
-
Time Social Interaction Rating



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), photo
s, 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 ra
ting (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
THE POWER OF SOCIAL
NETWORKING


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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 rating
s. 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).





OP
NE
EX
CO
AG
RTSI
NI
PE
ASC

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AG = Agreeableness Rating

CO = Co
nscientiousness Rating

EX = Extraversion Rating

NE = Neuroticism Rating

OP = Openness to Experience Rating






NAR
LON
SHY
RTSI
NI
PE
ASC

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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 “be
tter 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 th
an someone
THE POWER OF SOCIAL
NETWORKING


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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 bette
r treat them. This being possible since the
scores are based on psychological aspects of a person.

THE POWER OF SOCIAL
NETWORKING


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References

Who uses Facebook? An investigation into the relationship between the Big

Five, shyness,
narcissism,  loneliness,  and  Facebook  usage
,  
by  Tracii  R
yan  and  Sophia  Xenos,  
Computers  in  
Human  Behavior
,  Vol.  27,  No.  5.  (08  September  2011),  pp.  1658
-­‐
1664
 
NFL  Quarterback  Rating  Formula.
 
QB  Rating  Calc
.  http://www.nfl.com/help/quarterbackratingformula  
May  12,  2012