Dynamics of Internet-
mediated partnership
formation
Petter Holme
with Luìs Enrique Correa da Rocha,
Christofer Edling & Fredrik Liljeros

romantic & sexual
relations

romantic & sexual
relations
media

romantic & sexual
relations
media

romantic & sexual
relations
media
data

romantic & sexual
relations
media
data

romantic & sexual
relations
media
data

Computers can analyze survey data. Compared
with the internal working speed of a computer, the rate of
operation of its peripheral equipment—in particular, the
input and output mechanisms—is slow. (Simpson)
1961

1966
Computer matching studies. Despite the evidence
on the romantic nature of women ... the present data
indicate that in a first dating situation, men more often
than women experience romantic attraction for their
partners. (Coombs & Kenkel, J. Marriage & Family)
Computers can analyze survey data. Compared
with the internal working speed of a computer, the rate of
operation of its peripheral equipment—in particular, the
input and output mechanisms—is slow. (Simpson)
1961

1966
Computer matching studies. Despite the evidence
on the romantic nature of women ... the present data
indicate that in a first dating situation, men more often
than women experience romantic attraction for their
partners. (Coombs & Kenkel, J. Marriage & Family)
Computers can analyze survey data. Compared
with the internal working speed of a computer, the rate of
operation of its peripheral equipment—in particular, the
input and output mechanisms—is slow. (Simpson)
1961

1966
Computer matching studies. Despite the evidence
on the romantic nature of women ... the present data
indicate that in a first dating situation, men more often
than women experience romantic attraction for their
partners. (Coombs & Kenkel, J. Marriage & Family)
Computers can analyze survey data. Compared
with the internal working speed of a computer, the rate of
operation of its peripheral equipment—in particular, the
input and output mechanisms—is slow. (Simpson)
1961
1970 The information age /
information explosion. (Toffler)

1966
Computer matching studies. Despite the evidence
on the romantic nature of women ... the present data
indicate that in a first dating situation, men more often
than women experience romantic attraction for their
partners. (Coombs & Kenkel, J. Marriage & Family)
Computer communication democratize
information. Death of distance. Scientists
in obscure universities ... will be able to participate
in scientific discourse more readily. (Folk)
1977
Computers can analyze survey data. Compared
with the internal working speed of a computer, the rate of
operation of its peripheral equipment—in particular, the
input and output mechanisms—is slow. (Simpson)
1961
1970 The information age /
information explosion. (Toffler)
1967-77
Golden age of social network analysis.
Small-world experiment. Centrality indices.
Similarity indices. Strength of weak ties.

Computer communication & society.
As more and more people use computer-mediated
communication, its societal effects are becoming
critical research topics. (Kiesler, McGuire)
1984
Linguistic changes might occur as a result of
computer mediated communication. (Baron)1984
Internet Relay Chat Open chat-rooms.
Net.romances was a designated dating channel1988
Prostitution advertised on Usenet groups
alt.sex.services, later alt.sex.prostitution1986
Communicating emotions electronically. Is
electronic communication depersonalizing? … Communicators
must imagine their audience, for at a terminal it almost seems as
though the computer itself is the audience. (Kiesler, McGuire)
1982

1999
Scale-free networks.A large class of networks have
power-law degree distributions. Triggered search for
universal features & mechanisms (Barabási & Albert).
WWW dating sites. match.com1995
First scholarly work on IRCAnonymity make love-
seekers braver. Special netiquette develops. Internet
communication as a data source about social interaction. (Reid)
1991
Datamining. Ways to find patterns in
data beyond regression.late 1980’s
Data driven social network studies.
E-small-world, bursty dynamics, crowd intelligence2000’s
2003 Holme, Edling, Liljeros, Structure and time-evolution of an
Internet dating community, Social Networks 26:155–174.
Rocha, Liljeros, Holme, Information dynamics
shape the sexual networks of Internet-mediated
prostitution, PNAS 107:5706–5711.
2010

7
Romantic networks

P.Holme,C.R.Edling&F.Liljeros.
Structureandtime-evolutionofan
Internetdatingcommunity.
SocialNetworks26:155–174,2004.
You are logged in as:
user Z P20
You have one new message
Message box
Hey you Friday, July 5, 200
User A F20
Here User A has
space to write
about herself . . .
» Community /user A F
all in one place N
u

rC
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−0.05
0 100 200 300 400 500
t (days)
100 200 300 400 5000
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rewiredoriginal

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dynamics of ongoing
social relationships
Europhys. Lett. 64:427–

13
Sexual networks

a
Cumulativedistribution,P(k)
Number of partners, k
Females
Males
α
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totα
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Liljeros et al., 2001.
The Web of Human
Sexual Contacts Nature
411:908–909.
ba
Cumulativedistribution,P(k)
Cumulativedistribution,P(ktot)
Number of partners, k Total number of partners, ktot
totα
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Males
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Degree / activity correlations
Nordvik, Liljeros, 2006. Sexually Transmitted Diseases, 33:342–349.

Degree / activity correlations
Nordvik, Liljeros, 2006. Sexually Transmitted Diseases, 33:342–349.

16
Sexual networks
in prostitution

Who buys sex & why?
Pitts et al., 2004.Arch. Sex. Behav. 33:353–358.

Cultural differences
Wikipedia
legal and
regulated
legal but pimping,
brothels, etc. are illegal illegal unknown

Peculiar economics
Edlund et al., 2009. “The Wages of sin” working paper.

What determines the price?
Increasing the number of prostitutes by one adds to the totalp (i)Fm ipn
expenditure on prostitutes. If then the revenue per∗
p (i)F ! p (n)F ,m ipn npi
prostitute must fall; conversely, if the revenue must∗
p (i)F 1 p (n)F ,m ipn npi
increase. Formally,
∗
! 0 if p (i)F ! p (n)Fm ipn npi
∗′ ∗
p (n)F p 0 if p (i)F p p (n)F (13)npi m ipn npi
{ ∗
1 0 if p (i)F 1 p (n)F .m ipn npi
Condition (13) implies that there is a unique if∗
n ෈ (0, N )
and To see this, note that∗ ∗
p (0) 1 p (0) ϩ w(0) p (N ) ! p (N ) ϩ w(N ).m m
then and cross at most once since and∗ ′
p (n)F p (i) p (i) 1 0npi m m
if∗′ ∗
p (n)F p 0 p (i) p p (n)F .npi m npi
As before, if N is sufficiently large. Moreover,∗
p (0) 1 p (0) ϩ w(0)m
∗
p (N ) ! p (N ) (14)m
is a sufficient condition for To see that condition∗
p (N ) ! p (N ) ϩ w(N ).m
(14) holds, note that if the richest man buys the services fromn p N,
more than one prostitute; there are no wives, and Hence,∗
ˆp (N ) ! y(N ).
he would be willing to pay to one woman to be his wife∗
p (N ) 1 p (N )m
instead of his full-time prostitute. Q.E.D.
Edlund, Korn, 2002. A theory of
prostitution, J. Pol. Econ. 110:181–
214.

How is the information shared between sex-buyers.
What is the relation between different types of
prostitution?
What are the trends? Can we project into the future?
What are the implications for disease spreading?
What determines the price?
Human dynamics.

Rocha, Liljeros, Holme, 2010. PNAS 107, 5706-5711.
Elizabeth Pisani, http://www.wisdomofwhores.com/
Swedes make sex boring, even in Brazil
Another thumbs down for the Swedish model. Not
the leggy blonde, not even Sweden’s moralistic
approach to the sex trade. This one is the Swedish
research model, which has managed to turn the
fascinating subject of on-line rating of hookers by
Brazilian punters into something indescribably dull.

Rocha, Liljeros, Holme, 2010. PNAS 107, 5706-5711.
Elizabeth Pisani, http://www.wisdomofwhores.com/
Swedes make sex boring, even in Brazil
Another thumbs down for the Swedish model. Not
the leggy blonde, not even Sweden’s moralistic
approach to the sex trade. This one is the Swedish
research model, which has managed to turn the
fascinating subject of on-line rating of hookers by
Brazilian punters into something indescribably dull.

location

type of sex

date

grade

Metrics Buyers Sellers
Number of vertices 10,106 6,624
Size of largest component 9,652 6,158
Number of edges 40,895
Number of encounters 50,185
Original Randomized
Diameter of largest comp. 17 13.2 ± 0.1
Average distance 5.78 4.921 ± 0.002
Number of 4-cycles 231,439 64,360 ± 302
Assortativity −0.110 −0.0896 ± 0.0005

numberoffutureposts
0
10
20
30
40
50
−1.0 −0.5 0 0.5 1.0
/20,TG final
615≤s<20
20≤s<4
0 ≤ 4s<
number of posts
/2,TGfinalTfinal
0
0.2
0.4
0.6
0.8
1
1 3 10 30 100 300
Feedback

Degree distribution &
preferential attachment
1
1 10
K
1 10
K
1
p(k≥K)
p(k≥K)
0.1 1
sampling time
0.9
1
1.1
δ
0.9
1
1.1
δ
sampling time
0.1 1
sellers buyers
10�� 10��
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10��
0.1
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0.6
0.7
0.8
0.9
1.0
frequencyofnocondomuse
0.7
0.8
0.9
1.0
10 100
post number, τ post number, τ
1 10 100 1
frequencyofnocondomuse
sellers buyers
Trends in risky behavior

1
10
10
F
1
10
10
F
T (days)
~ T
0.5
~ T
0.5
T (days)
sellers buyers
~ T
1.2
~ T
0.6
~ T
0.6
~ T
1.2
10� 10� 10� 10�
10��10��
0.1 0.1
Detrended fluctuation analysis

Geography

LMA Bettencourt et al., PNAS 104:7301–7306 (2007).

LMA Bettencourt et al., PNAS 104:7301–7306 (2007).

fractionofedgesbetweencities
intercity dist. (km)
slope–2
10��
10��
10� 10�
numberofsellers
population size
sellers
slope110�
10�
10� 10�
numberofbuyers
population size
buyers
slope1
10� 10�
10�
10�
City size & spatial scaling

6,7,9
B
C
1,2,4,5
11
10,15
A
Temporal effects

time
6,7,9
B
C
1,2,4,5
11
10,15
A
Temporal effects

Empirical Randomized
0
0.2
0.4
0.6
0 200 400 600
Average�actionofinfected
Time (days)
Time-stamps randomized
0 200 400 600
Time (days)
800
Randomized tim� &
contacts, keeping
activity &
correlatio�
Temporal effects for disease spreading

0
0.2
0.4
0.6
0.01 0.1 1
Averageoutbreaksize
Transmission rate
0.18
0.20
0.22
0.24
0.26
0.28
0 300 600 900 1200
Crossingpoint
Initial Time (days)
ρ*
SIS Thresholds and convergence(?)

s.d. of c, σ
avg.numberofpartners/year,c
0.5 1 1.5 2
0.5
1
1.5
2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
relativedifferenceinR₀,d
Change in R₀

http://www.tp.umu.se/~holme/
Thank you!
Luìs Enrique Correa da Rocha
Christofer Edling
Fredrik Liljeros