Topographic analysis of an empirical human sexual network
Geoffrey Canright and Kenth Engø-Monsen, Telenor R&I, Norway
Valencia Remple, U of British Columbia, Vancouver, Canada
Theory meets reality
• Here we will combine two things:
• The ’topographic’, or ’regions-based’, theoretical
approach to analysis of epidemic spreading (ECCS04 and
ECCS05) (GSC/KEM)
+
• A detailed empirical network of human sexual contacts,
based on female sex workers (FSW) in Vancouver BC
(SNA 2006 + 2007) (VR—’Orchid’)
Our topographic picture (briefly)
• Eigenvector centrality (EVC)  ‘spreading power’
– High EVC  well connected to well connected nodes
• EVC is ‘smooth’  a topographic approach makes sense:
for any given graph, we find one or more ‘mountains’ (or
‘regions’), each with its most central node at the top
We call the top
node for each
region the ’Center’
• Region membership is determined by ‘steepest-ascent
path’ (on the steepest-ascent graph or SAG) to the
Center (top)
• Spreading within regions is fairly fast and predictable
• Spreading between regions may be neither of these
The Vancouver ’Orchid’ dataset
• Based on extensive surveys of female sex workers (FSW)
and their Clients
• Contacts between these, and with partners (and
sometimes partners of partners) were recorded
• 553 nodes, 1498 links
• 2 nodes are HIV positive; other STI’s found in 11 other
nodes
The Orchid graph — regions analysis
= male
= female
= HIVpos
The Orchid graph — regions analysis — SAG
= male
= female
A purely heterosexual graph is bipartite!
• Bipartite graph: two sets of nodes (eg, M and F); all
connections are between the two sets (M  F)
• We are accustomed to finding only a few regions in the
(non-bipartite) graphs we have studied (EX: 10 million
nodes, 1 region ...)
• In a purely bipartite graph, there are no triangles  the
graph is not as ’well connected’ as it could be otherwise
• The Orchid graph is ’mostly bipartite’ (only 11/1502 links
are homosexual); we conjecture that this is the reason
for the many (17) regions that we find
• Nevertheless we find the graph to be dominated by 3
large regions (totalling 517/553 nodes)
Conjecture: Centers tend to be confined to
one gender (M or F) due to bipartite
property
Here we
plot all
nodes
with at
least 20
partners
Center = large
Here, all Centers are men!
Our predictions
• When an infection reaches a region, it moves towards the
Center (’uphill’), and ’takes off’ when it reaches the Central
neighborhood
• That is, once the infection reaches the Central neighborhood of
a region, the entire region is ’lost’ (ie, rapidly infected)
• Movement between regions is heavily dependent on how well
connected the regions are
• In the Orchid graph, the strongest connections are
Grey  Red  Blue
• HIV is found in the Red region (2 hops from Center—bad
news), and at the Center of a small region (also 2 hops from
the Center of Red region!)  
• We expect it to be difficult to protect the Red region; also, the
strong connections to the other two are a problem!
Spreading simulation
start with Red HIV-positive node 233
Total
Red
Grey
Blue
fast take off
Protecting the Red region is difficult
• 237 dominates, but either HIV-pos node infects the Red region
fast
• Simulations with both infected look like those with just 237
•  if we must prioritize one for protection, it would be 237
• We have immunized the Red Center; no help!
• Reason: there remains a very dense Red Central neighborhood
•  we find no easy way to protect the Red region
• However the graph topology suggests that the Grey region can
be protected from infections coming from Red, via protecting the
Grey Center (node 117)
• We also find that infections from the Grey region are slowed
down by immunizing this same node
Spreading simulation
start with both HIV-positive nodes; immunize Grey Center node
No
immunization
Immunize
117
Grey region takes off later
Spreading simulation
start node 306 = STI, in Grey region
Immunize
the Grey
Center
Conclusions (thus far)
• The quasi-bipartite nature of the sexual contact network
has made our regions analysis a bit more interesting
• However, the main features we found in earlier work are
again found here
• The role of the region as a unit of analysis is clear
• In particular, the whole region is ”lost” once the Central
neighborhood is infected
• We find it difficult to protect the (big) Red region from the
HIV-infected nodes—they are too close to its Center
• However, we find that inoculating just one node can
significantly hinder Grey  Red spreading
Future work
1. Weight the links with realistic infection transmission
probabilities per unit time
a. Since these weights are disease dependent, we will get a distinct
adjacency matrix for each disease
b. The regions analysis is also sensitive to link weights
c. Thus, using realistic weights will make the regions analysis more
realistic, and hence more practical
2. Using realistic link weights, seek and test promising
protection strategies
a. We have not attempted to do that systematically here, due to
1.b. above
b. Strategies to be tested need not be limited to those suggested
by our analysis, since the simulations are ”agnostic”