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Peer influence and social contagion are key denominators in the adoption and participation of information spreading, such as news propagation, word-of-mouth or viral marketing. In this study, we argue that it is biased to only focus on the scale and coverage of information spreading, and propose that the level of influence reinforcement, quantified by the re-exposure rate, i.e., the rate of individuals who are repeatedly exposed to the same information, should be considered together to measure the effectiveness of spreading. We show that local network structural characteristics significantly affects the probability of being exposed or re-exposed to the same information. After analyzing trending news on the super large-scale online network of Sina Weibo (China's Twitter) with 430 million connected users, we find a class of users with extremely low exposure rate, even they are following tens of thousands of others; and the re-exposure rate is substantially higher for news with more transmission waves and stronger secondary forwarding. While exposure and re-exposure rate typically grow together with the scale of spreading, we find exceptional cases where it is possible to achieve a high exposure rate while maintaining low re-exposure rate, or vice versa., Comment: 16 pages,7 figures,1 table

Methicillin-resistant Staphylococcus aureus (MRSA) is a difficult-to-treat infection that only in the European Union affects about 150,000 patients and causes extra costs of 380 million Euros annually to the health-care systems. Increasing efforts have been taken to mitigate the epidemics and to avoid potential outbreaks in low endemic settings. Understanding the population dynamics of MRSA through modeling is essential to identify the causal mechanisms driving the epidemics and to generalize conclusions to different contexts. We develop an innovative high-resolution spatiotemporal contact network model of interactions between patients to reproduce the hospital population in the context of the Stockholm County in Sweden and simulate the spread of MRSA within this population. Our model captures the spatial and temporal heterogeneity caused by human behavior and by the dynamics of mobility within wards and hospitals. We estimate that in this population the epidemic threshold is at about 0.008. We also identify that these heterogeneous contact patterns cause the emergence of super-spreader patients and a polynomial growth of the epidemic curve. We finally study the effect of standard intervention control strategies and identify that screening is more effective than improved hygienic in order to cause smaller or null outbreaks.

During an epidemic control, the containment of the disease is usually achieved through increasing devoted resource to shorten the duration of infectiousness. However, the impact of this resource expenditure has not been studied quantitatively. Using the well-documented cholera data, we observe empirically that the recovery rate which is related to the duration of infectiousness has a strong positive correlation with the average resource devoted to the infected individuals. By incorporating this relation we build a novel model and find that insufficient resource leads to an abrupt increase in the infected population size, which is in marked contrast with the continuous phase transitions believed previously. Counterintuitively, this abrupt phase transition is more pronounced in the less contagious diseases, which usually correspond to the most fatal ones. Furthermore, we find that even for a single infection source, public resource needs to meet a significant amount, which is proportional to the whole population size to ensure epidemic containment. Our findings provide a theoretical foundation for efficient epidemic containment strategies in the early stage., Comment: 12 pages, 5 figures

Most centralities proposed for identifying influential spreaders on social networks to either spread a message or to stop an epidemic require the full topological information of the network on which spreading occurs. In practice, however, collecting all connections between agents in social networks can be hardly achieved. As a result, such metrics could be difficult to apply to real social networks. Consequently, a new approach for identifying influential people without the explicit network information is demanded in order to provide an efficient immunization or spreading strategy, in a practical sense. In this study, we seek a possible way for finding influential spreaders by using the social mechanisms of how social connections are formed in real networks. We find that a reliable immunization scheme can be achieved by asking people how they interact with each other. From these surveys we find that the probabilistic tendency to connect to a hub has the strongest predictive power for influential spreaders among tested social mechanisms. Our observation also suggests that people who connect different communities is more likely to be an influential spreader when a network has a strong modular structure. Our finding implies that not only the effect of network location but also the behavior of individuals is important to design optimal immunization or spreading schemes.

Quantitative social science is not only about regression analysis or, in general, data inference. Computer simulations of social mechanisms have a 60-year long history. They have been used for many different purposes -- to test scenarios, test the consistency of descriptive theories (proof-of-concept models), explore emergent phenomena, forecast, etc. In this essay, we sketch these historical developments, the role of mechanistic models in the social sciences, and the influences from the natural and formal sciences. We argue that mechanistic computational models form a common ground for social and natural sciences and look forward to possible future information flow across the social-natural divide., Comment: v3, many typos corrected

Sampling hidden populations is particularly challenging using standard sampling methods mainly because of the lack of a sampling frame. Respondent-driven sampling (RDS) is an alternative methodology that exploits the social contacts between peers to reach and weight individuals in these hard-to-reach populations. It is a snowball sampling procedure where the weight of the respondents is adjusted for the likelihood of being sampled due to differences in the number of contacts. In RDS, the structure of the social contacts thus defines the sampling process and affects its coverage, for instance by constraining the sampling within a sub-region of the network. In this paper we study the bias induced by network structures such as social triangles, community structure, and heterogeneities in the number of contacts, in the recruitment trees and in the RDS estimator. We simulate different scenarios of network structures and response-rates to study the potential biases one may expect in real settings. We find that the prevalence of the estimated variable is associated with the size of the network community to which the individual belongs. Furthermore, we observe that low-degree nodes may be under-sampled in certain situations if the sample and the network are of similar size. Finally, we also show that low response-rates lead to reasonably accurate average estimates of the prevalence but generate relatively large biases., Comment: 14 pages, 11 figures

Respondent-driven sampling (RDS) is frequently used when sampling hard-to-reach and/or stigmatized communities. RDS utilizes a peer-driven recruitment mechanism where sampled individuals pass on participation coupons to at most $c$ of their acquaintances in the community ($c=3$ being a common choice), who then in turn pass on to their acquaintances if they choose to participate, and so on. This process of distributing coupons is shown to behave like a new Reed-Frost type network epidemic model, in which becoming infected corresponds to receiving a coupon. The difference from existing network epidemic models is that an infected individual can not infect (i.e.\ sample) all of its contacts, but only at most $c$ of them. We calculate $R_0$, the probability of a major "outbreak", and the relative size of a major outbreak in the limit of infinite population size and evaluate their adequacy in finite populations. We study the effect of varying $c$ and compare RDS to the corresponding usual epidemic models, i.e.\ the case of $c=\infty$. Our results suggest that the number of coupons has a large effect on RDS recruitment. Additionally, we use our findings to explain previous empirical observations., Comment: 20 pages, 10 figures

Organizational growth processes have consistently been shown to exhibit a fatter-than-Gaussian growth-rate distribution in a variety of settings. Long periods of relatively small changes are interrupted by sudden changes in all size scales. This kind of extreme events can have important consequences for the development of biological and socio-economic systems. Existing models do not derive this aggregated pattern from agent actions at the micro level. We develop an agent-based simulation model on a social network. We take our departure in a model by a Schwarzkopf et al. on a scale-free network. We reproduce the fat-tailed pattern out of internal dynamics alone, and also find that it is robust with respect to network topology. Thus, the social network and the local interactions are a prerequisite for generating the pattern, but not the network topology itself. We further extend the model with a parameter $\delta$ that weights the relative fraction of an individual's neighbours belonging to a given organization, representing a contextual aspect of social influence. In the lower limit of this parameter, the fraction is irrelevant and choice of organization is random. In the upper limit of the parameter, the largest fraction quickly dominates, leading to a winner-takes-all situation. We recover the real pattern as an intermediate case between these two extremes., Comment: 15 pages, 4 figures

We investigate what structural aspects of a collection of twelve empirical temporal networks of human contacts are important to disease spreading. We scan the entire parameter spaces of the two canonical models of infectious disease epidemiology -- the Susceptible-Infectious-Susceptible (SIS) and Susceptible-Infectious-Removed (SIR) models. The results from these simulations are compared to reference data where we eliminate structures in the interevent intervals, the time to the first contact in the data, or the time from the last contact to the end of the sampling. The picture we find is that the birth and death of links, and the total number of contacts over a link, are essential to predict outbreaks. On the other hand, the exact times of contacts between the beginning and end, or the interevent interval distribution, do not matter much. In other words, a simplified picture of these empirical data sets that suffices for epidemiological purposes is that links are born, is active with some intensity, and die.

Objective: Lack of representative data about hidden groups, like men who have sex with men (MSM), hinders an evidence-based response to the HIV epidemics. Respondent-driven sampling (RDS) was developed to overcome sampling challenges in studies of populations like MSM for which sampling frames are absent. Internet-based RDS (webRDS) can potentially circumvent limitations of the original RDS method. We aimed to implement and evaluate webRDS among a hidden population. Methods and Design: This cross-sectional study took place 18 February to 12 April, 2011 among MSM in Vietnam. Inclusion criteria were men, aged 18 and above, who had ever had sex with another man and were living in Vietnam. Participants were invited by an MSM friend, logged in, and answered a survey. Participants could recruit up to four MSM friends. We evaluated the system by its success in generating sustained recruitment and the degree to which the sample compositions stabilized with increasing sample size. Results: Twenty starting participants generated 676 participants over 24 recruitment waves. Analyses did not show evidence of bias due to ineligible participation. Estimated mean age was 22 year and 82% came from the two large metropolitan areas. 32 out of 63 provinces were represented. The median number of sexual partners during the last six months was two. The sample composition stabilized well for 16 out of 17 variables. Conclusion: Results indicate that webRDS could be implemented at a low cost among Internet-using MSM in Vietnam. WebRDS may be a promising method for sampling of Internet-using MSM and other hidden groups. Key words: Respondent-driven sampling, Online sampling, Men who have sex with men, Vietnam, Sexual risk behavior

The timing patterns of human communication in social networks is not random. On the contrary, communication is dominated by emergent statistical laws such as non-trivial correlations and clustering. Recently, we found long-term correlations in the user's activity in social communities. Here, we extend this work to study collective behavior of the whole community. The goal is to understand the origin of clustering and long-term persistence. At the individual level, we find that the correlations in activity are a byproduct of the clustering expressed in the power-law distribution of inter-event times of single users. On the contrary, the activity of the whole community presents long-term correlations that are a true emergent property of the system, i.e. they are not related to the distribution of inter-event times. This result suggests the existence of collective behavior, possible arising from nontrivial communication patterns through the embedding social network., Comment: 26 pages, 7 figures

Respondent-driven sampling (RDS) is a commonly used substitute for random sampling when studying hidden populations, such as injecting drug users or men who have sex with men, for which no sampling frame is known. The method is an extension of the snowball sample method and can, given that some assumptions are met, generate unbiased population estimates. One key assumption, not likely to be met, is that the acquaintance network in which the recruitment process takes place is undirected, meaning that all recruiters should have the potential to be recruited by the person they recruit. Here we investigate the potential bias of directedness by simulating RDS on real and artificial network structures. We show that directedness is likely to generate bias that cannot be compensated for unless the sampled individuals know how many that potentially may have recruited them (i.e. their indegree), which is unlikely in most situations. Based on one known parameter, we propose an estimator for RDS on directed networks when only outdegrees are observed. By comparison of current RDS estimators' performances on networks with varying structures, we find that our new estimator, together with a recent estimator, which requires the population size as a known quantity, have relatively low level of estimate error and bias. Based on our new estimator, sensitivity analysis can be made by varying values of the known parameter to take uncertainty of network directedness and error in reporting degrees into account. Finally, we have developed a bootstrap procedure for the new estimator to construct confidence intervals., Comment: 22 pages, 1 table, 18 figures

The study of human interactions is of central importance for understanding the behavior of individuals, groups and societies. Here, we observe the formation and evolution of networks by monitoring the addition of all new links and we analyze quantitatively the tendencies used to create ties in these evolving online affiliation networks. We first show that an accurate estimation of these probabilistic tendencies can only be achieved by following the time evolution of the network. For example, actions that are attributed to the usual friend of a friend mechanism through a static snapshot of the network are overestimated by a factor of two. A detailed analysis of the dynamic network evolution shows that half of those triangles were generated through other mechanisms, in spite of the characteristic static pattern. We start by characterizing every single link when the tie was established in the network. This allows us to describe the probabilistic tendencies of tie formation and extract sociological conclusions as follows. The tendencies to add new links differ significantly from what we would expect if they were not affected by the individuals' structural position in the network, i.e., from random link formation. We also find significant differences in behavioral traits among individuals according to their degree of activity, gender, age, popularity and other attributes. For instance, in the particular datasets analyzed here, we find that women reciprocate connections three times as much as men and this difference increases with age. Men tend to connect with the most popular people more often than women across all ages. On the other hand, triangular ties tendencies are similar and independent of gender. Our findings can be useful to build models of realistic social network structures and discover the underlying laws that govern establishment of ties in evolving social networks., Comment: 10 pages, 8 figures

A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight according to a distribution that is allowed to depend on the degree of its vertex. Half-edges with the same weight are then paired randomly to create edges. An expression for the threshold for the appearance of a giant component in the resulting graph is derived using results on multi-type branching processes. The same technique also gives an expression for the basic reproduction number for an epidemic on the graph where the probability that a certain edge is used for transmission is a function of the edge weight. It is demonstrated that, if vertices with large degree tend to have large (small) weights on their edges and if the transmission probability increases with the edge weight, then it is easier (harder) for the epidemic to take off compared to a randomized epidemic with the same degree and weight distribution. A recipe for calculating the probability of a large outbreak in the epidemic and the size of such an outbreak is also given. Finally, the model is fitted to three empirical weighted networks of importance for the spread of contagious diseases and it is shown that $R_0$ can be substantially over- or underestimated if the correlation between degree and weight is not taken into account.

If we can lower the number of people needed to vaccinate for a community to be immune against contagious diseases, we can save resources and life. A key to reach such a lower threshold of immunization is to find and vaccinate people who, through their behavior, are more likely to become infected and effective to spread the disease than the average. Fortunately, the very behavior that makes these people important to vaccinate can help us finding them. People you have met recently are more likely to be socially active and thus central in the contact pattern, and important to vaccinate. We propose two immunization schemes exploiting temporal contact patterns. Both of these rely only on obtainable, local information and could implemented in practice. We show that these schemes outperform benchmark protocols in four real data sets under various epidemic scenarios. The data sets are dynamic, which enables us to make more realistic evaluations than other studies - we use information only about the past to perform the vaccination and the future to simulate disease outbreaks. We also use models to elucidate the mechanisms behind how the temporal structures make our immunization protocols efficient.

We study implications of the dynamical and spatial contact structure between Brazilian escorts and sex-buyers for the spreading of sexually transmitted infections (STI). Despite a highly skewed degree distribution diseases spreading in this contact structure have rather well-defined epidemic thresholds. Temporal effects create a broad distribution of outbreak sizes even if the transmission probability is taken to the hypothetical value of 100%. Temporal correlations speed up outbreaks, especially in the early phase, compared to randomized contact structures. The time-ordering and the network topology, on the other hand, slow down the epidemics. Studying compartmental models we show that the contact structure can probably not support the spread of HIV, not even if individuals were sexually active during the acute infection. We investigate hypothetical means of containing an outbreak and find that travel restrictions are about as efficient as removal of the vertices of highest degree. In general, the type of commercial sex we study seems not like a major factor in STI epidemics., Comment: 19 pages including 7 figures

Like many other social phenomena, prostitution is increasingly coordinated over the Internet. The online behavior affects the offline activity; the reverse is also true. We investigated the reported sexual contacts between 6,624 anonymous escorts and 10,106 sex-buyers extracted from an online community from its beginning and six years on. These sexual encounters were also graded and categorized (in terms of the type of sexual activities performed) by the buyers. From the temporal, bipartite network of posts, we found a full feedback loop in which high grades on previous posts affect the future commercial success of the sex-worker, and vice versa. We also found a peculiar growth pattern in which the turnover of community members and sex workers causes a sublinear preferential attachment. There is, moreover, a strong geographic influence on network structure-the network is geographically clustered but still close to connected, the contacts consistent with the inverse-square law observed in trading patterns. We also found that the number of sellers scales sublinearly with city size, so this type of prostitution does not, comparatively speaking, benefit much from an increasing concentration of people.

Researchers in many scientific fields make inferences from individuals to larger groups. For many groups however, there is no list of members from which to take a random sample. Respondent-driven sampling (RDS) is a relatively new sampling methodology that circumvents this difficulty by using the social networks of the groups under study. The RDS method has been shown to provide unbiased estimates of population proportions given certain conditions. The method is now widely used in the study of HIV-related high-risk populations globally. In this paper, we test the RDS methodology by simulating RDS studies on the social networks of a large LGBT web community. The robustness of the RDS method is tested by violating, one by one, the conditions under which the method provides unbiased estimates. Results reveal that the risk of bias is large if networks are directed, or respondents choose to invite persons based on characteristics that are correlated with the study outcomes. If these two problems are absent, the RDS method shows strong resistance to low response rates and certain errors in the participants' reporting of their network sizes. Other issues that might affect the RDS estimates, such as the method for choosing initial participants, the maximum number of recruitments per participant, sampling with or without replacement and variations in network structures, are also simulated and discussed., Comment: 21 pages, 17 figures, 1 table

We investigate the timing of messages sent in two online communities with respect to growth fluctuations and long-term correlations. We find that the timing of sending and receiving messages comprises pronounced long-term persistence. Considering the activity of the community members as growing entities, i.e. the cumulative number of messages sent (or received) by the individuals, we identify non-trivial scaling in the growth fluctuations which we relate to the long-term correlations. We find a connection between the scaling exponents of the growth and the long-term correlations which is supported by numerical simulations based on peaks over threshold. In addition, we find that the activity on directed links between pairs of members exhibits long-term correlations, indicating that communication activity with the most liked partners may be responsible for the long-term persistence in the timing of messages. Finally, we show that the number of messages, $M$, and the number of communication partners, $K$, of the individual members are correlated following a power-law, $K\sim M^\lambda$, with exponent $\lambda\approx 3/4$., Comment: 13 pages, 16 figures, 1 table

Networks portray a multitude of interactions through which people meet, ideas are spread, and infectious diseases propagate within a society. Identifying the most efficient "spreaders" in a network is an important step to optimize the use of available resources and ensure the more efficient spread of information. Here we show that, in contrast to common belief, the most influential spreaders in a social network do not correspond to the best connected people or to the most central people (high betweenness centrality). Instead, we find: (i) The most efficient spreaders are those located within the core of the network as identified by the k-shell decomposition analysis. (ii) When multiple spreaders are considered simultaneously, the distance between them becomes the crucial parameter that determines the extend of the spreading. Furthermore, we find that-- in the case of infections that do not confer immunity on recovered individuals-- the infection persists in the high k-shell layers of the network under conditions where hubs may not be able to preserve the infection. Our analysis provides a plausible route for an optimal design of efficient dissemination strategies., Comment: 36 pages, 20 figures

Even though people in our contemporary, technological society are depending on communication, our understanding of the underlying laws of human communicational behavior continues to be poorly understood. Here we investigate the communication patterns in two social Internet communities in search of statistical laws in human interaction activity. This research reveals that human communication networks dynamically follow scaling laws that may also explain the observed trends in economic growth. Specifically, we identify a generalized version of Gibrat's law of social activity expressed as a scaling law between the fluctuations in the number of messages sent by members and their level of activity. Gibrat's law has been essential in understanding economic growth patterns, yet without an underlying general principle for its origin. We attribute this scaling law to long-term correlation patterns in human activity, which surprisingly span from days to the entire period of the available data of more than one year. Further, we provide a mathematical framework that relates the generalized version of Gibrat's law to the long-term correlated dynamics, which suggests that the same underlying mechanism could be the source of Gibrat's law in economics, ranging from large firms, research and development expenditures, gross domestic product of countries, to city population growth. These findings are also of importance for designing communication networks and for the understanding of the dynamics of social systems in which communication plays a role, such as economic markets and political systems., Comment: 20+7 pages, 4+2 figures

We introduce an immunization method where the percentage of required vaccinations for immunity are close to the optimal value of a targeted immunization scheme of highest degree nodes. Our strategy retains the advantage of being purely local, without the need of knowledge on the global network structure or identification of the highest degree nodes. The method consists of selecting a random node and asking for a neighbor that has more links than himself or more than a given threshold and immunizing him. We compare this method to other efficient strategies on three real social networks and on a scale-free network model, and find it to be significantly more effective.

We apply percolation theory to a recently proposed measure of fragmentation $F$ for social networks. The measure $F$ is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after removing a fraction $q$ of nodes and the total number of pairs in the original fully connected network. We compare $F$ with the traditional measure used in percolation theory, $P_{\infty}$, the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods from percolation, we study Erd\H{o}s-R\'{e}nyi (ER) and scale-free (SF) networks under various types of node removal strategies. The removal strategies are: random removal, high degree removal and high betweenness centrality removal. We find that for a network obtained after removal (all strategies) of a fraction $q$ of nodes above percolation threshold, $P_{\infty}\approx (1-F)^{1/2}$. For fixed $P_{\infty}$ and close to percolation threshold ($q=q_c$), we show that $1-F$ better reflects the actual fragmentation. Close to $q_c$, for a given $P_{\infty}$, $1-F$ has a broad distribution and it is thus possible to improve the fragmentation of the network. We also study and compare the fragmentation measure $F$ and the percolation measure $P_{\infty}$ for a real social network of workplaces linked by the households of the employees and find similar results., Comment: submitted to PRE

Travel restrictions may reduce the spread of a contagious disease that threatens public health. In this study we investigate what effect different levels of travel restrictions may have on the speed and geographical spread of an outbreak of a disease similar to SARS. We use a stochastic simulation model of the Swedish population, calibrated with survey data of travel patterns between municipalities in Sweden collected over three years. We find that a ban on journeys longer than 50 km drastically reduces the speed and the geographical spread of outbreaks, even with when compliance is less than 100%. The result is found to be robust for different rates of inter-municipality transmission intensities. Travel restrictions may therefore be an effective way to mitigate the effect of a future outbreak.

Yet in spite of advances in hospital treatment, hospitals continue to be a breeding ground for several airborne diseases and for diseases that are transmitted through close contacts like SARS, methicillin-resistant Staphylococcus aureus (MRSA), norovirus infections and tuberculosis (TB). Here we extract contact networks for up to 295,108 inpatients for durations up to two years from a database used for administrating a local public healthcare system serving a population of 1.9 million individuals. Structural and dynamical properties of the network of importance for the transmission of contagious diseases are then analyzed by methods from network epidemiology. The contact networks are found to be very much determined by an extreme (age independent) variation in duration of hospital stays and the hospital structure. We find that that the structure of contacts between in-patients exhibit structural properties, such as a high level of transitivity, assortativity and variation in number of contacts, that are likely to be of importance for the transmission of less contagious diseases. If these properties are considered when designing prevention programs the risk for and the effect of epidemic outbreaks may be decreased.

We analyze the growth statistics of Swedish trade unions and find a universal functional form for the probability distribution of growth rates of union size, and a power law dependence of the standard deviation of this distribution on the number of members of the union. We also find that the typical size and the typical number of local chapters scales as a power law of the union size. Intriguingly, our results are similar to results reported for other human organizations of a quite different nature. Our findings are consistent with the possibility that universal mechanisms may exist governing the growth patterns of human organizations.

In a recent paper, James Holland Jones and Mark Handcock re-analyze two of the four datasets comprising a database, first analyzed by us, which records the number of distinct sexual partners for Swedish men and women. We argue that the claims of Jones and Handcock can be interpreted in a misleading fashion., Comment: 6 pages

Systems with two types of agents with a preference for heterophilous interaction produces networks that are more or less close to bipartite. We propose two measures quantifying the notion of bipartivity. The two measures--one well-known and natural, but computationally intractable; one computationally less complex, but also less intuitive--are examined on model networks that continuously interpolates between bipartite graphs and graphs with many odd circuits. We find that the bipartivity measures increase as we tune the control parameters of the test networks to intuitively increase the bipartivity, and thus conclude that the measures are quite relevant. We also measure and discuss the values of our bipartivity measures for empirical social networks (constructed from professional collaborations, Internet communities and field surveys). Here we find, as expected, that networks arising from romantic online interaction have high, and professional collaboration networks have low bipartivity values. In some other cases, probably due to low average degree of the network, the bipartivity measures cannot distinguish between romantic and friendship oriented interaction.

We present statistics for the structure and time-evolution of a network constructed from user activity in an Internet community. The vastness and precise time resolution of an Internet community offers unique possibilities to monitor social network formation and dynamics. Time evolution of well-known quantities, such as clustering, mixing (degree-degree correlations), average geodesic length, degree, and reciprocity is studied. In contrast to earlier analyses of scientific collaboration networks, mixing by degree between vertices is found to be disassortative. Furthermore, both the evolutionary trajectories of the average geodesic length and of the clustering coefficients are found to have minima., Comment: to appear in Social Networks

Many ``real-world'' networks are clearly defined while most ``social'' networks are to some extent subjective. Indeed, the accuracy of empirically-determined social networks is a question of some concern because individuals may have distinct perceptions of what constitutes a social link. One unambiguous type of connection is sexual contact. Here we analyze data on the sexual behavior of a random sample of individuals, and find that the cumulative distributions of the number of sexual partners during the twelve months prior to the survey decays as a power law with similar exponents $\alpha \approx 2.4$ for females and males. The scale-free nature of the web of human sexual contacts suggests that strategic interventions aimed at preventing the spread of sexually-transmitted diseases may be the most efficient approach., Comment: 7 pages with 2 eps figures. Latex file. For more details or for downloading the PDF file of the published article see http://polymer.bu.edu/~amaral/WebofContacts.html . For more results on teh structure of complex networks see http://polymer.bu.edu/~amaral/Networks.html