Structure of Romantic and Sexual relationship

[Pinu7]

I wish I had the raw data. These dots and strings are not enlightening. A more useful representation of the data would be "How many relationships-How many people exposed." Bar/line graph.

I have a good feeling it will be exponential.

It would also be better to just have a survey of sexual relationships instead of the other since romantic relationships DO NOT imply a sexual one.

 

[Huckleberry]

The text describes a non-romantic relationship as one in which the couple are having intercourse but not dating. I'm assuming that a romantic relationship involves intercourse and dating. If the study is to be used to apply STD prevention then it doesn't make sense otherwise.

(Romantic relationships were ones in which the students named the other as a romantic partner. Non-romantic sexual partners were those in which the participants said they had sexual intercourse, but were not dating).

“The students in this network are not unusual. They are just average students, and not extremely active sexually. So social policies that could help some of them protect themselves from STDs could break a lot of these chains that can lead to the spread of disease.”

 

[redargon]

If the study is to be used to apply STD prevention then it doesn't make sense otherwise.

If the study is to be used to apply STD prevention then it doesn't make sense anyway.

as I said earlier:

I notice it isn't time dependant. That is to say, that it does not show which relations come first. This makes the data a little less useful in disease spreading analysis. This is what I mean by eaxmple:
Person A has a relation with Person B and after that with Person C.
Person C has had 3 relations.
So, Person A has had in effect 5 relations (person B, Person C and the 3 relations of Person C (if they all occurred beforehand)) whereas even though Person B is connected to Person A, they have only had one relation as it occurred before Person A connected to person C.
I think this is an important thing to note when trying to track diseases.

 

[jobyts]

If the study is to be used to apply STD prevention then it doesn't make sense anyway.

as I said earlier:

The graph is not a TSP (Traveling Salesman's) problem. Also,
When they say it's applied to prevent STD, they don't mean how many people got STD from person X. And the pattern helps in creating effective strategy to prevent STD.
The following is the sex pattern they found different between adults and teenagers.

In adult populations, in which there are cores of sexually active people who are the main conduits of disease, you can focus education and other efforts to this select group.

But in the case of adolescents, “there aren’t any hubs to target, so you have to focus on broad-based interventions,” Moody said. “You can’t just focus on a small group.”

The interpretation of the graph is, in adults, it's more of a hub-spoke topology, whereas among teens, it's more random.

 

[Huckleberry]

If the study is to be used to apply STD prevention then it doesn't make sense anyway.

Yeah, you're right. I was only speculating on their definition of 'romantic relationship'. If they chose to include non-sexual dating as romantic relations then it would make even less sense. Including intercourse in their definition still doesn't improve upon their method.

The only time related reference I saw was that it is limited to partners within a 6 month period. It's pretty vague, but it makes for a pretty chart.

 

[BobG]

If the study is to be used to apply STD prevention then it doesn't make sense anyway.

as I said earlier:

It does if you're looking at things from a probability point of view. The people involved won't know the detailed sexual history of their partners (or whether the sex was protected or unprotected).

 

[Redbelly98]

I am pretty sure that the appearance of those connectons as a ring is an artifact of arbitrary organization. While factual, it has little meaning.

Well, I was just getting into this whole thread but now the mood is ruined.

 

[GeorginaS]

I can't think of another message board I've been a member of where a picture of dots and lines could generate four pages worth of discussion and analysis.

That's one reason why I like it here.

 

[jobyts]

Well, I was just getting into this whole thread but now the mood is ruined.

Yes, The initial mood was trying to find out who is the biggest stud and slut, and question like do they do orgies etc. (also Dave's attempt to imagine himself as the blue dot connected to 6 pinks , until he knew it's a 6 months graph, not a six year graph )

But later the talk changed to graph theory and STD

 

[CRGreathouse]

Yes I am, but you shouldn't go looking for special meaning into the big circle, because there's probably something similar in every group just by probability

I am pretty sure that the appearance of those connectons as a ring is an artifact of arbitrary organization. While factual, it has little meaning.

If you have a random set of dots laid out and make random connections, you get topological data minus spatial organization. Then you manually arrange all those branches and nodes to be as visually organized as possible, it will disproportionately highlight things like this. It's just unavoidable.

Actually I thought it was quite unusual for a random graph -- for as many connections as there are, I would expect a larger main component. It's only 1/4 to 1/3 the population.

 

[mXSCNT]

I ran some tests, adding edges randomly and independently of one another. If the expected number of hookups for any given person is around 1, for a few hundred people you do typically get one large component, which is almost a tree (very few cycles)--so perhaps the lack of cycles is not noteworthy.

My source code (python):

import random
from copy import deepcopy

# create a graph with numnodes nodes, where each edge has a probability
# of existing such that the expected number of edges to a given node
# is avgconnects
# graph is stored as an adjacency list dict
# no self-edges
def randgraph(numnodes,avgconnects):
    graph = {}
    nodes = range(numnodes)
    prob = float(avgconnects)/(numnodes-1)
    for x in nodes:
        graph[x] = set([])
    for x in nodes:
        for y in nodes[:x]:
            if random.random() <= prob:
                graph[x].add(y)
                graph[y].add(x)
    return graph

# create a random graph of boys and girls
# where boy nodes connect only to girl nodes
# and girl nodes connect only to boy nodes
# and the expected number of edges to any node is avgconnects
# (if the number of boys and girls is unequal,
#  this may result in higher or lower averages for each gender)
def boygirlgraph(boynum,girlnum,avgconnects):
    graph = {}
    boys = ['b' + str(x) for x in range(boynum)]
    girls = ['g' + str(x) for x in range(girlnum)]
    prob = float(avgconnects)*(boynum+girlnum)/(2*boynum*girlnum)
    
    for x in boys + girls:
        graph[x] = set([])
    for b in boys:
        for g in girls:
            if random.random() <= prob:
                graph[b].add(g)
                graph[g].add(b)
    return graph

# imperatively remove the node from the graph
# assumes all edges are bidirectional
def removenode(node,graph):
    for x in graph[node]:
        graph[x].remove(node)
    graph.pop(node)

# return a list of connected components, each component being a set of nodes
# the largest components appear first in the list
def componentlist(graph):
    components = []
    tmpgraph = deepcopy(graph)
    while len(tmpgraph) > 0:
        (node,adj) = tmpgraph.iteritems().next()
        curcomp = set([])
        def descend(node):
            adj = tmpgraph[node]
            curcomp.add(node)
            for x in adj:
                if not x in curcomp:
                    descend(x)
        descend(node)
        components.append(curcomp)
        for x in curcomp:
            removenode(x,tmpgraph)
    components.sort(key=len,reverse=True)
    return components

# return the subgraph including only those nodes in the component given
def subgraph(component,graph):
    tmpgraph = {}
    for x in graph:
        if x in component:
            tmpgraph[x] = graph[x] & component
    return tmpgraph

# In a maximal connected component, how many edges would need to be removed
# to turn the component into a tree?
def numcycles(component, graph):
    nedges = 0
    for x in component:
        nedges += len(graph[x])
    nedges /= 2
    # tree has len(component) - 1 edges
    return nedges - len(component) + 1

# convert to graphviz/dot format
def dotfmt(graph):
    conns = [str(a) + ' -- ' + str(b) + ' ;' for a in graph for b in graph[a] if a < b]
    return "graph{\n" + '\n'.join(conns) + '\n}\n'

 

[BobG]

The guy connected to 9 pink dots can program in Python.

People who can program in Python are like porn stars.

People who can run Python programs on their computer are like porn star viewers.

A person who can't run Python programs on their computers is like a nerd with a Betamax.

 

[JasonRox]

I know what school my son is going to now.

 

[JasonRox]

I had boyfriends when I was in high school, but none of them were in high school. I guess there's no mapping for that.

I remember you telling me you liked younger men. Please tell me that happened later on in life.

 

[mcknia07]

I know what school my son is going to now.

Congrats, what are you naming him?

I'm not sure the world can handle a Jason JR.

 

[lisab]

Ah, http://xkcd.com/403/" explains a lot. It was all about esthetics.

 

[Pinu7]

Talking about this, xkcd's most recent comic is about physicists:

http://xkcd.com/613/

 

[wrongusername]

I'm kinda surprised there's a triangle in there. That means a girl had a relationship with both a girl and a boy during 6 months. So is she gay or straight?

Also, why are there no trapezoids?

 

[Borg]

I wonder if http://xkcd.com/540/" was applied?

 

[KingNothing]

HO-LY-****!

I had no idea people were that huge of sluts in high school. Some interesting notes:
-The biggest player had been with 8 girls
-The biggest slut had been with 5 guys

Also, does it not strike anyone else as a bit odd that this whole thing turned out to be planar? What does that imply for the nature of sexual relations?

 

[Redbelly98]

... why are there no trapezoids?

... does it not strike anyone else as a bit odd that this whole thing turned out to be planar?

Indeed. Where are the concave polygons, dodecahedra, and 4-dimensional hypercubes? Clearly the data has been doctored with.

 

[KingNothing]

Indeed. Where are the concave polygons, dodecahedra, and 4-dimensional hypercubes? Clearly the data has been doctored with.

Funny man, but I'm actually serious about the graph being 100% planar. It does seem strange to me, although I can't quite figure out what it means for sex.

 

[jobyts]

Funny man, but I'm actually serious about the graph being 100% planar. It does seem strange to me, although I can't quite figure out what it means for sex.

Were you hoping for a 3D pornographic picture of students having sex?

A 2D graph is enough to explain this relationship. We understand the 6 month time dimension is not shown here. Is that what you are talking about?

 

[Office_Shredder]

I think the question is it's curious that you can draw all those figures and avoid having to cross lines. For example, how would yo do this with a group of five people, all of who have had sex with each other?

 

[DaveC426913]

I see KingNothing's point. There could theoretically be groups of relationships that cannot be represented without crossing lines (or without requiring a third dimension to the graph).

Following OfficeShredders lead, I was about to ask what the simplest group of relationships is. OfficeShredder went for the group of five, but he missed the simpler one: 4 people. i.e. a tetrahedron.

4 people, all of whom have had romantic relationships with each other, cannot be represented in only 2 dimensions without crossing lines.

And that sheds light on the answer to KingNothing's point. This simplest relationship requires some statistically highly unlikely connections. 4 people all having had relationships with each other is unlikely enough, but to do so, it requires a minimum of two same-sex relationships.

  M
 /|\
F-+-F
 \|/
  M

 

[CRGreathouse]

Following OfficeShredders lead, I was about to ask what the simplest group of relationships is. OfficeShredder went for the group of five, but he missed the simpler one: 4 people. i.e. a tetrahedron.

4 people, all of whom have had romantic relationships with each other, cannot be represented in only 2 dimensions without crossing lines.

And that sheds light on the answer to KingNothing's point. This simplest relationship requires some statistically highly unlikely connections. 4 people all having had relationships with each other is unlikely enough, but to do so, it requires a minimum of two same-sex relationships.

  M
 /|\
F-+-F
 \|/
  M

No, K_4 is planar:

  M
 / \\
F---F|
 \ //
  M

Kuratowski's theorem says that a graph is planar iff it avoids K_5 (OfficeShredder's example) and K_3,3. I can't conveniently ASCII art K_3,3 for you, but it's much easier to imagine in this context since doesn't require homosexual relationships.

 

[DaveC426913]

No, K_4 is planar:

  M
 / \\
F---F|
 \ //
  M

Kuratowski's theorem says that a graph is planar iff it avoids K_5 (OfficeShredder's example) and K_3,3. I can't conveniently ASCII art K_3,3 for you, but it's much easier to imagine in this context since doesn't require homosexual relationships.

Oh, right. I had a hidden assumption of using only straight lines.

I don't know Kuratowskian math, but reading up on it, I can see that there are some groups that cannot be made, even allowing for circuitous paths. This seems highly reminescent of the 5 house puzzle. (Shoot, I can't remember what it's called. It the one where you have to join 5 people to 5 houses without any paths crossing.)

 

[CRGreathouse]

Minor (ha, ha) correction: planar graphs can't contain K_5 or K_3,3 or any subdivision of either. (Obvious only in my own head.)

I can see that there are some groups that cannot be made, even allowing for circuitous paths.

Well you can make them, just not on a plane without crossing.K_3,3 could be three males and three females, where each person is adjacent to/has had a romantic relationship with everyone of the opposite sex.