Using Social Networks to
Analyze Sexual Relations
by Amanda Dargie
Definitions
 Social
Network: using graph theory in a
way of analyzing social interactions
vertices: people
edges between vertices: connections between people
 “Sexual”
Network: a social network
representing sexual relationships between
people (edges between sexual partners)
What is the importance of “sexual” networks?
 The
development of “sexual” networks
enables researches to better analyze the
spread of sexually transmitted infection
and diseases
 By looking at the networks, one can see
the path or possible paths in which the
disease took in reaching a specific person
or population
In the networks we look at in this presentation we will denote black
vertices to be male while white vertices will be female.
Creating a Network…
• Start with a person (a
vertex)
• *Add adjacent vertices
representing their sexual
partners
• Repeat (*) until you are
satisfied with your network
(may be as big or a small as
you’d like)
You can also create a network by starting with two
infected people and creating a chain to see if they
are connected in any way…
• Start with the two
infected people
• *Add adjacent vertices
representing their sexual
partners
• Repeat (*) to see if you
can find a path between
the two original people
In this case, it doesn’t take us too long to
find a path connecting the two original
people. This path lets us analyze a possible
route for the infection to travel.
Example
We know originally that person A has the
infection, but the disease has now shown
up in person Z. If A did not have any
sexual contact with person Z, how did Z
contract the infection? Is it possible for
them to be linked?
Z
A



Begin by adding all
adjacent vertices to A
and Z (their sexual
partners)
*Then add all of those
people’s sexual partners
Repeat (*) until you
find a path connecting
the two original people
Z
A
From this network, we can conclude that it is a definite possibly that person
Z did contract the infection through a path of infected people originating at
person A
NOTE: It is not always possible to find a path between two vertices.
Other
times, there may be a path that is not found because of its length and
time it would take to find.
Different Components
Linear Component
Spiral Component
“A Snapshot of Teen Sex”
Chains of
Affection
Each dot represents a
BOY or GIRL at “Jefferson
High.” The lines that link
them represent romantic
and sexual relationships
that occurred over an 18month period. While
most of the teenagers had
had just one or two
partners, 288 of the 832
kids interviewed were
linked in a giant sexual
network.
Taken from TIME, Feb. 7, 2005
“A Snapshot of Teen Sex”
Other relationships
(If a pattern was observed more than once, numeral indicates frequency.)
9
2
Proportion, by gender, of the
school’s students who reported at
least one relationship
14 63
2
BOYS
GIRLS
61%
55%
Taken from TIME, Feb. 7, 2005
Graph Measures
In order to help researchers analyze
graphs efficiently, they use different
methods to measure a graph
Four examples of ways to measure a graph:



Degree Centrality
Betweenness Centrality
Closeness Centrality
Degree Centrality
Looking at the degree of a vertex to see how
important or “centralized” the vertex to the graph as
a whole
B
A
H
D
E
C
F
G
I
Since Vertex D has the most direct connections. It is
important to look at where these connections go, and
whether or not they connect vertices that are otherwise
unconnected. In this case the go to other vertices that are
all already connected to each other.
Betweenness Centrality
Looking at vertices that play an important role in
connecting other vertices to each other
B
A
H
D
E
C
F
G
I
Vertex F, although not connected to many other vertices
directly, plays an important role in connecting the graph.
If we look at this graph as a social network, F is the way
of communication between the people on the left side of
the graph (A,B,C,D,E) and the people on the right side
(G,H,I). News would not travel from one group of
people to the other without person F.
Closeness Centrality
Looking at vertices that have the shortest paths to other vertices
B
A
H
D
E
C
F
G
I
Although, vertices E and F have lesser degree than that of
vertex D, their ties allow them to access any other vertex
in the graph the fastest. Both have at most a path of
length 3 to another vertex in the graph.
Flow Centrality
(expands on the notion of the betweenness centrality)
Assumes that two vertices (people) will use all
pathways between them
B
A
H
D
E
C
F
G
I
Let’s look at people A and E for example.
If person D decided not to relay messages from A to E or vise versa, the
message could be sent through either person B or C.
In this case, all paths are the same length (2). It is possible to be of
different length.
Betweenness of a graph is measured by the proportion of the entire
flow between two people (or, through all the paths between them)
Other Measures…
 Other








graph measures include:
boundary spanners
peripheral players
network centralization
structural equivalence
cluster analysis
structural holes
E/I Ratios
Small Worlds
Problems in Social Network Analysis
 One
of the main problems with this
kind of analysis is not being able to
determine when a person had sexual
relations with another.
Example: If a person had relations with one partner and then later
on in time had relations with another who happened to be infected, the
person he/she first had relations with will not be susceptible to the
infection (since it was prior). However, when analyzing the network,
one who see only that the person had had relations with two people,
one who was infected and therefore the other must be.
Order of Relations:
D
G
A
E
B
F
C
H
1.
2.
3.
4.
5.
6.
7.
Person C and Person G
Person B and Person E
Person A and Person C
Person B and Person F
Person A and Person B
Person B and Person D
Person C and Person H
So who is infected?
INFECTED: A, B, C, D, H
D
G
A
E
B
F
C
H
Person A is the original infected Person
and therefore gives the infection to
Person B and Person C
 Person C had relations with Person G
before A and Person H after Person A,
therefore Person G is safe of infection
while Person H is not
 On the other side, Person B had
relations with Person E and Person F
before Person A and so they’re safe, but
Person D is not since B had relations
with D after A

**Since researchers do not usually know the time
sequences for a network, they are unable to come to
the kind of results we have here.**
For you to try…



Reports of an outbreak of and STI has spread throughout
a high school population
Administration wants to know who has been tested
positive for the infection and who they have had
relations with in order to find out who may be
susceptible
Here’s what they know:


Person A has tested positive for the infection and has been
sexually active with Person B, C and D
Person B has been sexually active with Person E
the Network…





Person A has tested positive for
the infection and has been
sexually active with Person B,
C and D
Person B has been sexually
active with Person E who has
been sexually active with
Person F and Person G
Person D has been sexually
active with Person H
Create a network with this
information
H
D
Here’s what they know so far:
A
B
C
F
E
G
Results: Persons B, C, D, E, F,
G and H could all essentially
be infected as a result of this
chain of relations