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? A Z

 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 A Z 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 18- month 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

Other relationships (If a pattern was observed more than once, numeral indicates frequency.) Proportion, by gender, of the school’s students who reported at least one relationship BOYSGIRLS 61%55% Taken from TIME, Feb. 7, 2005 “A Snapshot of Teen Sex”

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 Degree Centrality Betweenness Centrality Betweenness Centrality Closeness Centrality Closeness Centrality

Degree Centrality A B C D E F G H 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. 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. Looking at the degree of a vertex to see how important or “centralized” the vertex to the graph as a whole

Betweenness Centrality 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. 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. A B C D E F G H I Looking at vertices that play an important role in connecting other vertices to each other

Closeness Centrality 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. A B C D E F G H I Looking at vertices that have the shortest paths to other vertices

Flow Centrality 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) A B C D E F G H I (expands on the notion of the betweenness centrality) Assumes that two vertices (people) will use all pathways between them

Other Measures…  Other graph measures include: boundary spanners boundary spanners peripheral players peripheral players network centralization network centralization structural equivalence structural equivalence cluster analysis cluster analysis structural holes structural holes E/I Ratios E/I Ratios Small Worlds 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: 1.Person C and Person G 2.Person B and Person E 3.Person A and Person C 4.Person B and Person F 5.Person A and Person B 6.Person B and Person D 7.Person C and Person H A B C D H G F E

So who is infected?   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 A B C D H G F E INFECTED: A, B, C, D, H **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 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 Person B has been sexually active with Person E

the Network…  Here’s what they know so far: Person A has tested positive for the infection and has been sexually active with Person B, C and D 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 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 Person D has been sexually active with Person H  Create a network with this information A B C D E F G H Results: Persons B, C, D, E, F, G and H could all essentially be infected as a result of this chain of relations