World Journal of AIDS, 2013, 3, 1-9 Published Online March 2013 (
Topological and Historical Considerations for Infectious
Disease Transmission among Injecting Drug Users in
Bushwick, Brooklyn (USA)
Kirk Dombrowski1*, Richard Curtis1, Samuel Friedman2, Bilal Khan1
1Social Networks Research Group, John Jay College CUNY, New York, USA; 2National Development Research Institute, New York,
Email: *
Received December 13th, 2012; revised January 22nd, 2013; accepted January 31st, 2013
Recent interest by physicists in social networks and disease transmission factors has prompted debate over the topology
of degree distributions in sexual networks. Social network researchers have been critical of “scale-free” Barabasi-Albert
approaches, and largely rejected the preferential attachment, “rich-get-richer” assumptions that underlie that model.
Instead, research on sexual networks has pointed to the importance of homophily and local sexual norms in dictating
degree distributions, and thus disease transmission thresholds. Injecting Drug User (IDU) network topologies may differ
from the emerging models of sexual networks, however. Degree distribution analysis of a Brooklyn, NY, IDU network
indicates a different topology than the spanning tree configurations discussed for sexual networks, instead featuring
comparatively short cycles and high concurrency. Our findings suggest that IDU networks do in some ways conform to
a “scale-free” topology, and thus may represent “reservoirs” of potential infection despite seemingly low transmission
Keywords: Social Network Analysis; Injecting Drug Users; Scale-Free Networks
1. Introduction
Recent interest by physicists in social networks and their
relationship with disease transmission factors has prom-
pted debate among social network theorists over the ex-
tent to which social networks conform more closely to
general structural principles or to local social norms. This
paper examines a smaller subset of this debate, and asks
whether Injecting Drug User (IDU) networks responsible
for the transmission of sexually transmitted and blood-
borne diseases look more like topologies recently labeled
“scale-free” by network theorists [1], or whether they are
more like sexual networks, which have been shown to
conform mainly to social principles like homophily and
other specifically local norms [2]. This is important be-
cause the answer to this question bears strongly on inter-
vention, prevention, and treatment strategies as they ap-
ply to IDU networks, and, to the extent that IDU net-
works continue to overlap with larger society in critical
health related ways, bears on larger questions of public
health and disease transmission more generally [3].
What follows is a reanalysis of data collected between
1991 and 1993 in the Bushwick neighborhood of Brook-
lyn, New York, on the social networks of injecting drug
users (IDUs) [4]. Our analysis employs analytical strate-
gies developed in the last few years by physicists work-
ing on what have come to be called “scale-free” networks,
as developed by Barabasi and Albert [5,6]. Partly be-
cause our data were not collected with such an analysis
in mind, throughout the paper we pose the findings and
conclusions as “suggested,” noting that several problems
preclude more firm conclusions, and likewise note that
this comparison leaves many aspects of IDU networks
unexplained. Yet the apparent similarities between the
network structure of the Bushwick IDU network and
structures examined by Barabasi, Albert and others,
prompt us to conclude that scale-free modeling can help
elicit critical differences between IDU network topolo-
gies and those associated with sexual networks. Our re-
sults indicate that IDU networks may in fact represent the
sorts of structural reservoirs of HIV and other blood-
borne and sexually transmitted diseases at issue in the
debates between physicists and sociologists, and thus
require special consideration for prevention/transmission/
intervention planners. What’s more, if IDU networks do
in fact conform more closely to general structural princi-
ples than to local norms, police intervention strategies of
*Corresponding author.
Copyright © 2013 SciRes. WJA
Topological and Historical Considerations for Infectious Disease Transmission among
Injecting Drug Users in Bushwick, Brooklyn (USA)
the early 1990s employed in New York to suppress IDU
networks ironically may have contributed to stronger
network integration and thus potentially greater risk of
disease transmission and network robustness. These con-
siderations are discussed in more detail below.
2. Sexual, IDU, and “Scale-Free” Networks
Scale-Free modeling has, in last decade, been developed
for a number of existing, real world networks, from the
World-Wide-Web [7], to academic citation patterns, to
the research partnerships of large pharmaceutical compa-
nies [8,9]. It has also been proposed for disease networks
[10,11], but here it has been critically received by many
social network theorists [12]. Analytical work on sexual
networks by social network researchers has more re-
cently tended to reject purely structural models in favor
of models that feature homophily and local norms as the
main organizing principles [2]; though see [13,14]. Sta-
tistical tests on existing sexual network data sets by Jones,
Handcock, and Holland have found that physicists’ mod-
els do not meet “best-fit maximum likelihood estimates”
for many short term sexual networks [12], which tend
toward other sorts of distributions. In multi-model tests,
scale free models seem to fit best those portions of sexual
network topology with high levels of connectivity
[12,13,15], and less well for low degree nodes (i.e. those
with few sexual partners). Further, in cases where scale
free models do fit well, the degree distributions of those
networks are quite different from most naturally occur-
ring scale free networks, such as those discussed by Ba-
rabasi and others. Likewise, Bearman, Moody and Stovel
[2] have shown that sexual networks lack the high levels
of concurrence characteristic of, say, the Internet or the
World-Wide-Web, showing instead that sexual networks
look more like “spanning tree” graphs, with few (usually
quite long) cycles.
IDU networks, however, differ from sexual networks
in important ways, as they usually involve high concur-
rency, and short cycles. This is mainly due to the pres-
ence of a demonstrable “core” of highly connected users
[16-18], producing short cycles and marked differences
in edge degree value between core and periphery. This
suggests that IDU networks, even where they contain
sexual behavior among users, may operate according to
different organizing principles than ordinary sexual net-
works, and thus contain different epidemiological dy-
namics. The specific features of those epidemiological
dynamics go beyond the purpose of the current paper,
though the influence of network cores on such issues as
HIV prevalence and transmission rates has been explored
in previous published work based on the Bushwick IDU
network [4,16,17]. Here we propose only an examination
of the degree distribution of the Bushwick IDU network,
with the intention of showing that IDU networks differ
from sexual networks in regard to the types of topologi-
cal features often associated with disease transmission.
2.1. The SFHR Data
The collection and analysis of the data in the Social Fac-
tors for HIV Risk (SFHR) study is presented in much
more detail in Friedman et al. Social Networks, Drug
Injectors Lives, and HIV/AIDS [4]. The data resulted
from sociological, ethnographic, and epidemiological
research into the drug and sexually related behaviors
among drug injectors, as well as HIV and Hepatitis B
exposure patterns for 767 injecting drug users in the
Bushwick area of Brooklyn NY. Data were gathered over
the course of 2 plus years, and analyzed in the book men-
tioned above and a number of related articles. Several
social network papers were published as a result of this
research, which firmly demonstrate the importance of
network analysis among injecting drug users [16,17]. A
social network diagram of the dyadic (person-to-person)
links elicited in the Bushwick network is available in
Figure 1. These links indicate contact via one or more
“risk” behaviors: specifically, those respondents who
injected drugs together or who engaged in sex with each
other in the context of drug use in the thirty days prior to
the interview. In prior analyses of this data, degree dis-
tribution was not systematically examined.
For purposes of the current paper, several areas of the
SFHR study data collection are of principal concern.
During the survey portion of the study, respondents were
asked to estimate the number of people they had injected
drugs with over the last 30 days. This was coded as INJP
(for “injection partners”) in the study. The responses here
varied considerably, with many respondents giving round
number figures and very rough estimates, and known
hubs sometimes giving very low estimates. This is not
surprising. Limitations of data gathered by “global item”
questions and ego-centered networks are well known
[19], and here are likely magnified by the illegal and so-
cially stigmatized nature of some of the behaviors in-
volved. Thus to more accurately gage the injecting be-
haviors beyond those simply reported by respondents’
initial estimates, an additional network measure of re-
spondent out-degree links was analyzed. Respondents
were asked for a list of twenty close associates and
whether the respondent had injected drugs or engaged in
sex with that particular person in the last 30 days [20,21].
From these data, in-degree figures could also be calcu-
lated for each respondent, based on the number of per-
sons in the study who named the subject as a recent part-
ner. These network data created a dyad-based network
picture which served as a partial check on the INJP esti-
mates. Arc directions in Figure 1 indicate the direction
Copyright © 2013 SciRes. WJA
Topological and Historical Considerations for Infectious Disease Transmission among
Injecting Drug Users in Bushwick, Brooklyn (USA)
Copyright © 2013 SciRes. WJA
Figure 1. The risk network of injecting drug users discovered by the SFHR project in Bushwick, Brooklyn (USA) 1991-1993.
of the reports able to be verified by research staff from
the list of study respondents [20]. Names of those outside
of the study group or whose identities could not be veri-
fied are not included in this diagram or the dyad data
discussed below.
Where partners could be identified, the network inter-
view process thus produced data on two kinds of social
links or “dyads.” The first are “out-directed” arcs (coded
“DyadAC”), where the interviewee, person A, identifies
person C as a recent injecting/sex partner. One can thus
visualize the report creating a directed arc from A to C.
Yet this same information also creates an in-directed arc
or dyad connection (coded “DyadCA”) for person C (the
“receiver”, if you will, of the injection/sex partnering
reported by person A). One would expect that, when in-
terviewed, the indicated partner, “C” would then name
the original source, “A” as an injection partner as well. In
that case, out-directed arcs revealed in the network inter-
view by one respondent would be matched by in-directed
arcs from others. Examples of these sorts of linkages are
apparent in Figure 1. In a situation of full disclosure,
simultaneous interviews, and 100% research effective-
ness, in-degree and out-degree values (Σ DyadAC and Σ
DyadCA) would be identical in number for every re-
spondent (and, ideally, would match the INJP number
given by the respondent). This was, however, not always
the case, particularly for network “hubs”.
As mentioned above, some of the most widely cited
injecting partners themselves gave low estimates of their
number of partners (i.e. low INJP number), and identified
few—sometimes zero—out-directed connections (i.e. a
low Σ DyadAC). Where these respondents tended to ap-
pear in the network data was in other people’s reports of
their injecting partners (i.e. high numbers of in-di- rected
connections, i.e. Σ DyadCA). For this reason, it seemed
critical to create a weighted average for each respondent
of what would, under ideal conditions, consist of three
identical figures (INJP, Σ DyadAC, Σ DyadCA; where
INJP is, again, the number of self-reported injection
partners, Σ DyadAC is the number of people identified
by respondent “A” within the last 30 days as injection
related partners—as far as could be identified as part of
the study group by the research team—and Σ DyadCA
being the number of partnerings with “A” reported by
other respondents in the study group).
To compensate for the various problems described
above, the three injector partner factors were combined
to create a composite Mean Injection Total (MInjTot) for
each of the 767 research respondents. That is, MInjTot
figures were calculated for each individual (j) according
to the following formula:
MInjTot 3
ACDyadAC meanDyadAC
CA DyadCA.
MInjTotj is then rounded to the nearest integer value.
This formula constitutes a weighted average of the three
numbers (INJPj, Σ DyadACj, and Σ DyadCAj) for re-
spondent “j”, using the ratio of the average of all initial
Topological and Historical Considerations for Infectious Disease Transmission among
Injecting Drug Users in Bushwick, Brooklyn (USA)
total estimates (mean INJP) to the average of each dyad
type (mean Σ DyadAC and mean Σ DyadCA) as the re-
spective weighting factors. It should be noted, however,
that this likely reflects an under-reporting of injection
related partnering behaviors. The dyad research used
only the names of 20 associates, resulting in an artificial
ceiling of 20 for out-dyads (DyadAC) and, as such, a
hidden but systemic constraint on DyadCA, especially
for larger and medium sized hubs. As a result, for net-
work hubs, both DyadCA and DyadAC (each of which
would ideally equal the INJP estimate) will likely be
lower than the INJP. A second factor is that, for some
respondents, their involvement in other networks outside
of the study area meant that those links would necessarily
go unreported in the in-degree Dyad data, and thus their
DyadCA estimate would be an undercount. The compos-
ite number, by including the dyad data, thus likely repre-
sents an under-reporting of network connectedness when
those connections were to networks outside of Bushwick,
as in-directed links include only those to others in the
Bushwick network that could be identified as such by the
research team.These factors necessarily minimize the
firmness of the conclusions discussed below. Yet, as
above, the justification for the creation of a composite
MInjTot number was that, as suspected, the in-directed
dyad data often produced levels of individual intercon-
nectedness that went unreported or underreported in both
the out-directed dyad data and INJP respondent esti-
For purposes of the following model, injectors were
treated as individual nodes, j, while an event of injec-
tion/sex partnering was considered a link, and the total
number of links for each respondent, kj, calculated ac-
cording the MInjTot formula given above. As will be
seen below, kj numbers ranged from 0 to 35, with highest
numbers of respondents having low numbers of links (a
mode of 2). Respondents were then sorted by their re-
spective number of links kj and the total number of re-
spondents, ni, for each respective k value was determined.
The number of respondents ni for a given number of links
ki are given in Figure 2.
2.2. Scale-Free Networks
The first widely recognized paper on scale-free networks
by Barabasi and Albert appeared in 1999 [6], with a sub-
sequent full mathematical treatment and review of sub-
sequent findings in 2002 [1]. In their original research on
the World-Wide-Web (WWW), they found that the dis-
tribution of links (“arcs”) between webpages (“vertices”)
seems to follow a “power law distribution.” Such a dis-
tribution, they noted, is very different from those con-
forming to Poisson curves or random graphs, upon which
much prior network modeling depended, and this obser-
Figure 2. Number of users n (y-axis) with composite MIn-
jTot, number of partners k (x-axis).
vation encouraged them to consider whether something
other than a largely random, statistically normal distribu-
tion of connections was at work in this network. Subse-
quent research revealed many naturally occurring net-
works with apparent power law degree distributions,
similar to the WWW, further prompting Barabasi and
Albert to wonder whether identical, unusual network
dynamics were responsible for a range of naturally oc-
curring networks.
In graphs conforming to power law distributions, it is
possible to calculate a reasonably accurate measure of
the distribution of the connectedness of the various
nodes/vertices in the network. As above, this is referred
to as the “degree distribution,” and it amounts to a graph
of the number of nodes/vertices with the specified num-
ber of connections. On such a graph it is possible to cal-
culate the “decay coefficient” of the graph, in effect a
measure of the differential interconnectedness of the
various nodes in the network. In the group of naturally
occurring networks identified by Barabasi and Albert,
networks exhibited recurring decay coefficients at or
around 2 [1].
To account for the regularity of this finding, Barabasi
and Albert proposed a model of self-organizing networks
where new nodes are added through time according to a
linear preferential attachment or “rich-get-richer” strat-
egy [1,5,6,9], meaning that new nodes entering the net-
work establish links to existing nodes in linear proportion
to the number of links the latter already possess. In
computer simulations of growing networks, Barabasi and
Albert found that after a short time, linear preferential
attachment strategies achieved steady decay coefficients
between 2 and 3, and that the addition of new nodes after
that point did not alter the shape (or “topology”) of the
graph, at least as far as the value of the decay coefficient
(λ) was concerned. This ability, to grow steadily without
changing their topology, prompted Barabasi and Albert
to label these sorts of networks “scale-free,” to highlight
the fact that they achieved topological stability regardless
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Topological and Historical Considerations for Infectious Disease Transmission among
Injecting Drug Users in Bushwick, Brooklyn (USA)
of their network size or the addition of new nodes and
links, provided the rules of linear preferential attachment
held steady.
Such theoretical networks demonstrate a number of
characteristics in common with naturally occurring net-
works beyond sharing decay coefficient values around 2.
The first is that they are relatively impervious to error or
failure—meaning that the removal of a high number of
randomly selected nodes does not affect the topology of
the network (or the value of the decay coefficient). This
feature is referred to as network “robustness.” Yet they
also demonstrate “vulnerability to attack”, such that net-
work connectivity will fail (and the decay coefficient
cross over a threshold into a dispersed and poorly inte-
grated network) when a relatively low proportion of
nodes are removed from the network, provided those
taken out were “hubs” (i.e. nodes with high numbers of
links). And finally, scale free networks exhibit “small
world” characteristics [22], meaning that the shortest
path between any two nodes turns out to be quite small,
even in very large networks.
Based on these characteristics, a number of researchers
[7,10,11,13,14,23] argued that if sexual networks and
other infection networks in general conformed to a
scale-free distribution, then sexually transmitted diseases
could persist in sexual network populations despite van-
ishingly small transmission thresholds due to the pres-
ence of a small but significant population with high
numbers of links (i.e. high numbers of partners at risk for
infection). This would be an effect of network robustness
inherent in the structure of the network. Likewise, May
and Lloyd [24] point out that the risk associated with
membership in the network could be lowered dramati-
cally not by the removal of large numbers of participants,
but rather by focusing on altering the behavior of “hubs,”
i.e. those with the greatest number of partners (i.e. taking
advantage of the network’s “vulnerability to attack”).
And finally, scale free theorists in general have pointed
out that the small world character of these networks
would mean that stemming infection in one segment of
the population would meet with little lasting success, as
re-infection remained only a few short network steps
away, due to the nearness of many members of the net-
work to many others [11]. As above, there is consider-
able debate about these findings as they apply to sexual
networks, and our purpose is not to address this issue
directly, but rather to ask whether the Bushwick IDU
network conforms to a scale free topology, where such
issues may apply more directly. If so, then many of the
conclusions applied by scale free theorists to sexual net-
works as a whole might better apply to IDU networks
The process of establishing the decay coefficient for a
naturally occurring network (like the WWW) involves
sorting nodes by the number of links they possess, then
counting the number of nodes/vertices with a given num-
ber of links/edges. If we call ni the number of nodes in
the network with ki links, the decay coefficient λ of the
particular network can then be ascertained by plotting the
Log of n versus the Log of k for all values of i above 0,
and taking the slope of the resulting line...or in other
If P(k) ~ k−λ in a network where the highest number of
links for any node is t, then
loglog for ,,
nk kkk
 t
k (2)
where ni = number of nodes with edges ki. The slope of
the line in a plot of Log n versus Log k is thus the decay
coefficient λ, which represents, again, a formal measure
of the degree distribution of the network.
3. Results
Looking back at Figure 2, we note the apparent power
law distribution of the data. A log/log (base 10) graph of
the data from Figure 2 is available in Figure 3, and the
regression line of this data is indicated on the graph. As
discussed above, its slope is the decay coefficient λ for
the degree distribution in Figure 2. In this graph, λ = 1.8
(with a Pearson’s r value of 0.947, and an adjusted r-
square value of 0.891).
From this graph we note that MInjTot figures conform
well to a log linear representation: the Pearson’s r value
indicating a close association of the points. A second
immediate observation is that the value for λ = 1.8 is
close to that discovered for a host of real-world networks
by Barabasi, Albert and others: comparable decay coeffi-
cients were found for networks such as Hollywood actor
collaborations λactor = 2.3, the World-Wide-Web λwww-in =
2.1, λwww-out = 2.4, the metabolic network of E.coli bacte-
ria λecoli = 2.2, Internet Domains λdomain = 2.1, phone calls
λphone = 2.1, Co-authorship among neurologists λneuro =
2.1, or mathematicians λmath = 2.5, or other academics
Figure 3. Log/Log (base 10) graph of Figure 2.
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Topological and Historical Considerations for Infectious Disease Transmission among
Injecting Drug Users in Bushwick, Brooklyn (USA)
λspires = 1.2 [1, p. 51]. It is also worth noting that the value
is well below that normally discussed for sexual net-
works, i.e. where λ usually equals somewhere between 3
and 4 [10,14,15]. This will be discussed in greater detail
below. Equally clear is the “hubbed” nature of the net-
work, with wide differences in the distribution of links
among nodes, and a significant population having many
times the average (kavg = 3.0) and modal (kmode = 2)
number of links. Indeed, in Figure 2, 42 of the 767 re-
spondents (5% of the total network) accounted for 508/
1789 (about 28%) of the total links in the network, with a
range of k-values from 7 to 35.
A comparison with previously published ethnographic
and social network analyses of this same population
helps establish the representativeness of MInjTot formula.
Ethnographic observation indicates that the three most
“linked” individuals according to the MInjTot formula
are identifiable respondents who show up as central hubs
in a social network of “core” participants compiled from
observation data (described fully in [18]) and from social
network “Seidman k-core” analyses of this same popula-
tion [4,16]. In Figure 3, the most linked respondents,
respectively from right to left (high to low) on the x-axis,
correspond to respondents with identification numbers 16,
29, and 91 in Figure 1, with respondents 7, 10, 13, 21,
23, 26, 31, 42, 46, 83, 102, 210, 259 appearing in the top
25 most linked hubs according to the MInjTot formula as
well. Many of these same individuals also appear in the
ethnographic/observational core of this same network [18,
p. 236] and are clear hubs in the network diagram of
Figure 1 (again, drawn entirely from the dyad data). In-
deed, the ethnographic research component of the origi-
nal SFHR study identified respondents 16, 29 and 42
from Figure 1 as locally well-known shooting gallery
operators and central players in the Bushwick drug scene
[18, p. 235], a point we will return to below.
Network data on these and other individuals also
shows the ability of the composite MInjTot formula to
respond to a variety of reporting scenarios: respondent 16
estimated a total of 35 partners in the last 30 days, iden-
tifying 6 other members of the study (DyadAC) and be-
ing identified as such by 28 other study participants
(DyadCA), and respondent 29 estimated 30 partners,
identified 8 (DyadAC) and was identified by 19 (Dy-
adCA). Yet respondents 26 and 42, each gave self-re-
ports of low numbers of partners (8 and 1 respectively),
which masked high in-degree values (17 and 26 in-de-
gree values, respectively). They also appear in the model
as highly connected hubs in Figures 2 and 3. And finally,
in a somewhat opposite case, respondent 91’s estimate of
84 injection/sex partners was not matched by high Dy-
adAC (6) or CA (1), which may indicate a preponderance
of partners outside of the Bushwick network, or removal
from the network during the study period or a desire to
impress the interviewer with his status as an important
person in the network. As a result, this individual appears
with higher overall degree in Figures 2 and 3 than indi-
cated in Figure 1, but not as high as she would be in a
graph based solely on self-reported INJP figures. Alto-
gether, the composite formula was able to identify key
players in the network despite high variability in report-
ing profiles, and produce network structures borne out by
prior network analysis and ethnographic observation.
4. Discussion
With the representativeness of the graph established and
its similarities to other naturally occurring scale free
networks apparent, part of what must be addressed is
what is achieved by doing a “scale-free” analysis, as this
is often misperceived (and misadvertised). The model
above might be termed a “scale-free analysis” in the fol-
lowing sense; it is an analysis of the degree distribution
of a network that shows it to conform to the type of de-
gree distribution that Barabasi and Albert found could be
reproduced by means of simple, linear preferential at-
tachment. For the Bushwick IDU network, this is not
surprising at a very general level, given that IDU net-
work members ordinarily become members of a particu-
lar injector network via someone who was already part of
it. Indeed, ethnographic observation points out that some
of the more central figures in the Bushwick network,
apart from shooting gallery operators, were individuals
who functioned as connectors between core members and
new or more marginal network members [18].
While the purpose of such a comparison with Bara-
basi-Albert degree distributions is primarily suggestive,
and while degree distribution graphs are only one meas-
ure of network topology (and many other network pa-
rameter measures are possible: see [16] for Seidman k-
core distribution analysis of this same population), nev-
ertheless, the suggestion that IDU networks contain pref-
erential attachment dynamics is important, as it differen-
tiates them from findings about sexual networks [2], and
implicates them in important disease transmission dy-
namics [10,13,14]. Past research demonstrates the exis-
tence of a core-periphery structure, short cycles, and high
concurrency in the Bushwick IDU network [4,16], all of
which contrast strongly with the spanning tree models of
sexual networks described by Bearman, Moody and
Stoval. Such characteristics indicate that the “small
world” characteristics typical of scale free networks
could very well be present in the Bushwick IDU network.
This is critical as injection sharing and sexual contact
associated with injecting drug networks are already
known as important vectors for disease transmission,
further indicating that unique transmission dynamics may
Copyright © 2013 SciRes. WJA
Topological and Historical Considerations for Infectious Disease Transmission among
Injecting Drug Users in Bushwick, Brooklyn (USA)
take place among them that deserve serious attention [3].
As above, in small world networks, the network topology
itself can be responsible for preserving a high level of
system-wide risk even when disease prevalence is re-
duced to near zero levels.
The decay coefficient for the Bushwick IDU network
is interesting in this way as well. This is, as far as we
know, one of few cases in the disease transmission lit-
erature where the power-law decay coefficient of a dis-
ease transmission network is at or below 2. In contrast,
sexual networks usually demonstrate decay coefficients
of three or more [10,13-15]. May and Lloyd [24] have
shown mathematically that in disease transmission net-
works, topologies with decay co-efficient values below 3
indicate that there will always be someone in the popula-
tion-with enough contacts to spread the disease, inde-
pendent of population-wide disease transmission prob-
abilities. The possibility that IDU networks represent
such a group would then require special attention, con-
firming conclusions suggested by other analyses of this
data as well [25] that unique dynamics related to network
structure are at work. Indeed, from these graphs there is a
reasonable suggestion that IDU networks represent the
sorts of reservoirs of infection hypothesized by scale-free
That being said, it is important to note that, like sexual
networks, IDU networks do nevertheless conform to lo-
cal norms of risk behavior [4] and particular local events.
Yet these too must be understood to take place within a
specific structural framework. Evidence of this may be
present in Figure 3 as well. Of particular interest is that,
in Figure 3, the distribution of data points in relation to
the best fit line shows a clear deviation pattern. In Figure
3, those points to the left of the midpoint value of the
x-axis (logk = 0.8) tend to be above the regression line,
while those to the right of the midpoint value tend to be
below it, with the exceptions of a few points at the high-
est k values. This would indicate that the decay coeffi-
cient of 1.8 is in fact lowered by the several points at the
very far right (the highest values) on the x-axis, which
stretch the x-intercept of the regression line to the right,
and lessen its slope. At a superficial level, this point
bears out the claim by scale-free and small world theo-
rists (see [22]) that, in networks with highly differential
levels of connectedness, a few individuals with high
numbers of links (in Figure 3, this is four individuals)
can significantly alter the topology of the network.
As importantly, however, this aspect of the topology
of Figure 3 indicates that a few individuals at the far
right side of the graph represent a level of individual in-
terconnectedness kj above that predicted by a “scale-free”
distribution. When graphs of the model were repeated
without these 4 points, they return a decay coefficient of
λ = 2.1, a near perfect topological match for the scale free
model. Given this, the source of the deviation of these
four points (again, representing respondents 16, 29, 91,
and 162 in Figure 1) from the ideal-typical scale free
model is of particular interest. One central reason for this
deviation is suggested by ethnographic and interview
data, which points to changes in the Bushwick drug
market at the time of the study. During the 1991-1993
time frame, New York City as a whole [26], and Bush-
wick in particular, were undergoing a change in drug
interdiction regimes aimed at closing down “open air”
drug markets and injection locations [27]. This strategy
involved broad “sweeps” in which outdoor users were
routinely arrested for small amounts of drug possession.
As places serving as outdoor drug use locations were
systematically pursued by law enforcement, outdoor drug
use became increasingly precarious, and indoor, more
discreet drug use locations (shooting galleries) grew in
importance as a result [28,29]. Local estimates place
them at 5 or 6 in Bushwick at any given time over the
course of the two year study, and fluidity among loca-
tions was constant as interdiction turned toward these
locations as well.
Ethnographic observations and interviews with re-
spondents in the Bushwick study confirm that many of
the major network nodes identified in Figures 2 and 3 by
the composite MInjTot figure turned out to be either
shooting gallery operators (again respondents 16, 26, 29,
and 42), or close associates of these same individuals
who served as injection specialists or good vein locators,
for example, or runners for various kinds of equipment,
or recruiters for gallery operators (which included re-
spondents 7, 13, 31, 46, 91, 102), most of whom are
identifiable in Figure 1, and figure significantly as
“hubs” in Figures 2 and 3. The exaggerated centrality of
high-end hubs suggests to us that police interdiction
strategies may have strengthened the hub-like nature of
gallery operators, as network hubs found their centrality
enhanced by significant numbers of clients in search of
safe injection locales. This was particularly true for His-
panic gallery operators, whose greater tie-in to the local
community made the re-establishing of gallery locations
and reconstruction of a network of users both more likely
and quicker despite enforced mobility and occasional
removal from the network [27]. Beyond this, those who
remained within the Bushwick network across the entire
study period by avoiding arrest and other complications
were further able to accumulate high numbers of links.
As suggested by the data in Figure 3, then, interdic-
tion/enforcement strategies may thus have boosted the
level of interconnectedness for gallery operators and as-
sociated hubs beyond that predicted by self-organizing,
scale-free models, increasing network interconnectedness
Copyright © 2013 SciRes. WJA
Topological and Historical Considerations for Infectious Disease Transmission among
Injecting Drug Users in Bushwick, Brooklyn (USA)
and pushing the network as a whole toward a more
“fat-tailed” distribution.
Without comparable topological data for the periods
before or after 1991-1993 study period and a period of
peak police activity, observations like these are mostly
speculative. Never the less, by further heightening the
“hubbed” nature of the network, enforcement strategies
arguably increased the “small world” nature of the net-
work (shortening network distances across which infec-
tions pass), and the robustness of the network it-
self—meaning that police “sweeps” of users were further
rendered moot in terms of disrupting the network struc-
ture and interconnectedness.
5. Remaining Questions
As a final comment, it is also worth repeating that pref-
erential attachment, Barabasi-Albert models do not ac-
count for new links created by already established net-
work actors to others also already in the network. Nor do
they account for the effects of particular nodes disap-
pearing from the network. Do their former partners go on
to form new links? If so, to whom? Does preferential
attachment hold in aging networks (initial evidence is
that it does not; see Albert and Barabasi [1]? These are
critical features of IDU networks that likely also require
different sorts of attachment models, and likely quite
different sorts of network parameterization to detect.
Despite this, what remains critical here is the possibil-
ity that IDU networks conform to a topology quite dif-
ferent from that of sexual networks, despite the fact that
they remain linked to sexual networks (and thus repre-
sent areas of significant risk to the non-IDU population
[3,25]). The topological findings demonstrated here ex-
tend those already discussed for the SFHR data, and ar-
gue once again for special attention and special under-
standing of IDU networks and their structural (as well as
behavioral) uniqueness, and question the viability and
impact of interdiction strategies that do not address stru-
ctural dynamics [30].
6. Acknowledgements
Support for the original data collection was provided by
the National Institute on Drug Abuse grant DA06723
“Social Factors and HIV Risk” and grant P30DA11041
“Center for Drug Use and HIV Research.” The New
York State Department of Health AIDS Institute assisted
in drawing serum samples, HIV testing, and referrals.
The views expressed herein do not necessarily reflect the
positions of these institutes. This project was also sup-
ported by NIH/NIDA Challenge Grant 1RC1DA028476-
01/02 awarded to the CUNY Research Foundation and
John Jay College, CUNY. The opinions, findings, and
conclusions or recommendations expressed in this publi-
cation are those of the authors and do not necessarily
reflect those of the National Institute of Health/National
Institute on Drug Abuse.
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