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Networked populations consist of inhomogeneous individuals connected via relational ties. The individuals typically vary in multivariate attributes. In some cases primary interest focuses on individual attributes and in others the understanding of the social structure of the ties. In many circumstances both are of interest, as is their relationship. In this paper we consider this last, most general, case. We model the joint distribution of social ties and individual attributes when the population is only partially observed. Of central interest is when the population is surveyed using a network sampling design. A second situation is when data about a subset of the ties and/or the individual attributes is unintentionally missing. Exponential-family random network models (ERNM)s are capable of specifying a joint statistical representation of both the ties of a network and individual attributes. This class of models allow the nodal attributes to be modeled as stochastic processes, expanding the range and realism of exponential-family approaches to network modeling. In this paper we develop a theory of inference for ERNMs when only part of the network is observed, as well as specific methodology for partially observed networks, including non-ignorable mechanisms for network-based sampling designs. In particular, we consider data collected via contact tracing, of considerable importance to infectious disease epidemiology and public health.

Respondent-driven sampling (RDS) is a method for sampling from a target population by leveraging social connections. RDS is invaluable to the study of hard-to-reach populations. However, RDS is costly and can be infeasible. RDS is infeasible when RDS point estimators have small effective sample sizes (large design effects) or when RDS interval estimators have large confidence intervals relative to estimates obtained in previous studies or poor coverage. As a result, researchers need tools to assess whether or not estimation of certain characteristics of interest for specific populations is feasible in advance. In this paper, we develop a simulation-based framework for using pilot data-in the form of a convenience sample of aggregated, egocentric data and estimates of subpopulation sizes within the target population-to assess whether or not RDS is feasible for estimating characteristics of a target population. in doing so, we assume that more is known about egos than alters in the pilot data, which is often the case with aggregated, egocentric data in practice. We build on existing methods for estimating the structure of social networks from aggregated, egocentric sample data and estimates of subpopulation sizes within the target population. We apply this framework to assess the feasibility of estimating the proportion male, proportion bisexual, proportion depressed and proportion infected with HIV/AIDS within three spatially distinct target populations of older lesbian, gay and bisexual adults using pilot data from the caring and Aging with Pride Study and the Gallup Daily Tracking Survey. We conclude that using an RDS sample of 300 subjects is infeasible for estimating the proportion male, but feasible for estimating the proportion bisexual, proportion depressed and proportion infected with HIV/AIDS in all three target populations.

The random walk technique, which has a reputation for excellent performance, is one method for complex networks sampling. However, reducing the input data size is still a considerable topic to increase the efficiency and speed of this algorithm. The two approaches discussed in this paper, the no-retracing and the seed node selection algorithms, inspired the development of random walk technique. The Google PageRank method is integrated with these different approaches. Input data size is decreased while critical nodes are preserved. A real database was used for this sampling. Significant sample characteristics were also covered, including average clustering coefficient, sampling effectiveness, degree distribution, and average degree. The no-retracing method, for example, performs better. The efficiency increases even further when the no-retracing technique is combined with the Google PageRank. When choosing between public transportation and aircraft, for example, these algorithms might be used since time is crucial. Additionally, these algorithms are more energy-efficient methods that were looked at.

The network scale-up method is a promising technique that uses sampled social network data to estimate the sizes of epidemiologically important hidden populations, such as sex workers and people who inject illicit drugs. Although previous scale-up research has focused exclusively on networks of acquaintances, we show that the type of personal network about which survey respondents are asked to report is a potentially crucial parameter that researchers are free to vary. This generalization leads to a method that is more flexible and potentially more accurate. In 2011, we conducted a large, nationally representative survey experiment in Rwanda that randomized respondents to report about one of 2 different personal networks. Our results showed that asking respondents for less information can, somewhat surprisingly, produce more accurate size estimates. We also estimated the sizes of 4 key populations at risk for human immunodeficiency virus infection in Rwanda. Our estimates were higher than earlier estimates from Rwanda but lower than international benchmarks. Finally, in this article we develop a new sensitivity analysis framework and use it to assess the possible biases in our estimates. Our design can be customized and extended for other settings, enabling researchers to continue to improve the network scale-up method.

The network scale-up method is a promising technique that uses sampled social network data to estimate the sizes of epidemiologically important hidden populations, such as sex workers and people who inject illicit drugs. Although previous scale-up research has focused exclusively on networks of acquaintances, we show that the type of personal network about which survey respondents are asked to report is a potentially crucial parameter that researchers are free to vary. This generalization leads to a method that is more flexible and potentially more accurate. In 2011, we conducted a large, nationally representative survey experiment in Rwanda that randomized respondents to report about one of 2 different personal networks. Our results showed that asking respondents for less information can, somewhat surprisingly, produce more accurate size estimates. We also estimated the sizes of 4 key populations at risk for human immunodeficiency virus infection in Rwanda. Our estimates were higher than earlier estimates from Rwanda but lower than international benchmarks. Finally, in this article we develop a new sensitivity analysis framework and use it to assess the possible biases in our estimates. Our design can be customized and extended for other settings, enabling researchers to continue to improve the network scale-up method.

Recently, there has been growing interest in social network analysis. Graph models for social network analysis are usually assumed to be a deterministic graph with fixed weights for its edges or nodes. As activities of users in online social networks are changed with time, however, this assumption is too restrictive because of uncertainty, unpredictability and the time-varying nature of such real networks. The existing network measures and network sampling algorithms for complex social networks are designed basically for deterministic binary graphs with fixed weights. This results in loss of much of the information about the behavior of the network contained in its time-varying edge weights of network, such that is not an appropriate measure or sample for unveiling the important natural properties of the original network embedded in the varying edge weights. stochastic graphs, in which weights associated with the edges are random variables, can be a suitable model for complex social network. In this paper, according to the principle that Social networks are one of the cases where the distribution of links to nodes is according to the power law that we proposed Levy's initial flight automation sampling algorithm for random graphs, which is a good model for complex social networks. Using Levy Flight instead of gait-based learning that guarantees part of the solution is not separate from the present solution, therefore, it endores an optimizer tolerance, local optimal tolerance, and early convergence. In order to study the performance of the proposed sampling algorithms, several experiments are conducted on real and synthetic stochastic graphs. These algorithms 'performance is evaluated based on the relative cost, Kendall correlation coefficient, Kolmogorov–Smirnov D statistics, and relative error. [ABSTRACT FROM AUTHOR]

There are two distinct types of domains, design- and cross-classes domains, with the former extensively studied under the topic of small-area estimation. In natural resource inventory, however, most classes listed in the condition tables of national inventory programs are characterized as cross-classes domains, such as vegetation type, productivity class, and age class. To date, challenges remain active for inventorying cross-classes domains because these domains are usually of unknown sampling frame and spatial distribution with the result that inference relies on population-level as opposed to domain-level sampling. Multiple challenges are noteworthy: (1) efficient sampling strategies are difficult to develop because of little priori information about the target domain; (2) domain inference relies on a sample designed for the population, so within-domain sample sizes could be too small to support a precise estimation; and (3) increasing sample size for the population does not ensure an increase to the domain, so actual sample size for a target domain remains highly uncertain, particularly for small domains. In this paper, we introduce a design-based generalized systematic adaptive cluster sampling (GSACS) for inventorying cross-classes domains. Design-unbiased Hansen-Hurwitz and Horvitz-Thompson estimators are derived for domain totals and compared within GSACS and with systematic sampling (SYS). Comprehensive Monte Carlo simulations show that (1) GSACS Hansen-Hurwitz and Horvitz-Thompson estimators are unbiased and equally efficient, whereas thelatter outperforms the former for supporting a sample of size one; (2) SYS is a special case of GSACS while the latter outperforms the former in terms of increased efficiency and reduced intensity; (3) GSACS Horvitz-Thompson variance estimator is design-unbiased for a single SYS sample; and (4) rules-ofthumb summarized with respect to sampling design and spatial effect improve precision. Because inventorying a mini domain is analogous to inventorying a rare variable, alternative network sampling procedures are also readily available for inventorying cross-classes domains. [ABSTRACT FROM AUTHOR]

Respondent-Driven Sampling is a widely-used method for sampling hard-to-reach human populations by link-tracing over their social networks. Inference from such data requires specialized techniques because the sampling process is both partially beyond the control of the researcher, and partially implicitly defined. Therefore, it is not generally possible to directly compute the sampling weights for traditional design-based inference, and likelihood inference requires modeling the complex sampling process. As an alternative, we introduce a model-assisted approach, resulting in a design-based estimator leveraging a working network model. We derive a new class of estimators for population means and a corresponding bootstrap standard error estimator. We demonstrate improved performance compared to existing estimators, including adjustment for an initial convenience sample. We also apply the method and an extension to the estimation of HIV prevalence in a high-risk population.

The study of hard-to-reach populations presents significant challenges. Typically, a sampling frame is not available, and population members are difficult to identify or recruit from broader sampling frames. This is especially true of populations at high risk for HIV/AIDS. Respondent-driven sampling (RDS) is often used in such settings with the primary goal of estimating the prevalence of infection. In such populations, the number of people at risk for infection and the number of people infected are of fundamental importance. This article presents a case-study of the estimation of the size of the hard-to-reach population based on data collected through RDS. We study two populations of female sex workers and men-who-have-sex-with-men in El Salvador. The approach is Bayesian and we consider different forms of prior information, including using the UNAIDS population size guidelines for this region. We show that the method is able to quantify the amount of information on population size available in RDS samples. As separate validation, we compare our results to those estimated by extrapolating from a capture-recapture study of El Salvadorian cities. The results of our case-study are largely comparable to those of the capture-recapture study when they differ from the UNAIDS guidelines. Our method is widely applicable to data from RDS studies and we provide a software package to facilitate this.

We study the problem of identifying a set of key nodes from a network when limited knowledge about its structure is available. Most studies assume complete knowledge of the given network when identifying a set of key nodes, but in current practice, networks of interest are often too huge to obtain their entire topological structures. When the complete structure of a network is not available, network sampling strategies are often used to obtain a partial structure of the network. We investigate how network sampling strategies affect the problem of identifying a key node set. Specifically, we investigate the effect of conventional network sampling strategies on the solutions found for two types of key node set identification problems: the minimum $p$ -median problem and the influence maximization problem. Our results show that when the network is obtained using crawl-based network sampling strategies, both the minimum $p$ -median and the influence maximization problems are effectively solved by simple heuristic algorithms with sampling ratios in the 10-20% range. We also find that among three conventional sampling strategies (random sampling, random walk sampling, and sample edge counts) checked in this paper, random walk sampling is the most robust strategy in terms of effectively identifying the key node sets of diverse types of networks.

Social networks are streaming, diverse and include a wide range of edges so that continuously evolves over time and formed by the activities among users (such as tweets, emails, etc.), where each activity among its users, adds an edge to the network graph. Despite their popularities, the dynamicity and large size of most social networks make it difficult or impossible to study the entire network. This paper proposes a sampling algorithm that equipped with an evaluator unit for analyzing the edges and a set of simple fixed structure learning automata. Evaluator unit evaluates each edge and then decides whether edge and corresponding node should be added to the sample set. In The proposed algorithm, each main activity graph node is equipped with a simple learning automaton. The proposed algorithm is compared with the best current sampling algorithm that was reported in the Kolmogorov-Smirnov test (KS) and normalized L1 and L2 distances in real networks and synthetic networks presented as a sequence of edges. Experimental results show the superiority of the proposed algorithm.

• An online and nonuniform timeslicing strategy that enhances temporal and streaming network visualization. • Timeslicing reduces visual clutter and optimizes global pattern identification. • Evaluation through case studies using two real-world networks with distinct characteristics. [Display omitted] Visual analysis of temporal networks comprises an effective way to understand the network dynamics. It facilitates the identification of patterns, anomalies, and other network properties, thus resulting in fast decision making. The amount of data in real-world networks, however, may result in a layout with high visual clutter due to edge overlapping. This is particularly relevant in the so-called streaming networks , in which edges are continuously arriving (online) and in non-stationary distribution. All three network dimensions, namely node, edge , and time , can be manipulated to reduce such clutter and improve readability. This paper presents an online and nonuniform timeslicing method that enhances temporal and streaming network analyses. We conducted experiments using two real-world networks to compare our method against uniform and nonuniform timeslicing strategies. The results show that our method automatically selects timeslices that effectively reduce visual clutter in periods with bursts of events. As a consequence, decision making based on the identification of global temporal patterns becomes faster and more reliable. [ABSTRACT FROM AUTHOR]

Respondent-Driven Sampling (RDS) is n approach to sampling design and inference in hard-to-reach human populations. It is often used in situations where the target population is rare and/or stigmatized in the larger population, so that it is prohibitively expensive to contact them through the available frames. Common examples include injecting drug users, men who have sex with men, and female sex workers. Most analysis of RDS data has focused on estimating aggregate characteristics, such as disease prevalence. However, RDS is often conducted in settings where the population size is unknown and of great independent interest. This paper presents an approach to estimating the size of a target population based on data collected through RDS. The proposed approach uses a successive sampling approximation to RDS to leverage information in the ordered sequence of observed personal network sizes. The inference uses the Bayesian framework, allowing for the incorporation of prior knowledge. A flexible class of priors for the population size is used that aids elicitation. An extensive simulation study provides insight into the performance of the method for estimating population size under a broad range of conditions. A further study shows the approach also improves estimation of aggregate characteristics. Finally, the method demonstrates sensible results when used to estimate the size of known networked populations from the National Longitudinal Study of Adolescent Health, and when used to estimate the size of a hard-to-reach population at high risk for HIV.

Respondent-Driven Sampling (RDS) is n approach to sampling design and inference in hard-to-reach human populations. It is often used in situations where the target population is rare and/or stigmatized in the larger population, so that it is prohibitively expensive to contact them through the available frames. Common examples include injecting drug users, men who have sex with men, and female sex workers. Most analysis of RDS data has focused on estimating aggregate characteristics, such as disease prevalence. However, RDS is often conducted in settings where the population size is unknown and of great independent interest. This paper presents an approach to estimating the size of a target population based on data collected through RDS. The proposed approach uses a successive sampling approximation to RDS to leverage information in the ordered sequence of observed personal network sizes. The inference uses the Bayesian framework, allowing for the incorporation of prior knowledge. A flexible class of priors for the population size is used that aids elicitation. An extensive simulation study provides insight into the performance of the method for estimating population size under a broad range of conditions. A further study shows the approach also improves estimation of aggregate characteristics. Finally, the method demonstrates sensible results when used to estimate the size of known networked populations from the National Longitudinal Study of Adolescent Health, and when used to estimate the size of a hard-to-reach population at high risk for HIV.

Abstract This article discusses the possibilities and constraints of designing an identical or at least comparable sampling strategy across different European countries. It is based on expert reviews from six European Union member states that discuss the possibilities of sampling migrants in their respective countries. The country sample includes two countries from Northern Europe (Sweden, Denmark), two from Continental Europe (Germany, The Netherlands), and two from Southern Europe (Spain, Italy). After a discussion of various definitions of the target population and an overview of existing strategies to sample them, it is investigated which of them can be used in the six countries analyzed in the expert reviews. The focus is on probability samples and the use of population registers, while other sampling strategies are only briefly touched upon. The analysis shows that even with only six European countries an identical register-based sampling design is difficult. The authors propose that, by focusing on sampling immigrants in cities, researchers can better implement sampling strategies which result in comparable samples.

This article presents the results of a pilot feasibility study comparing two alternative recruitment approaches based on Respondent Driven Sampling using initial seeds selected from a US nationally representative panel, AmeriSpeak, to augment the number of lesbian, gay, bisexual, and transgender (LGBT) respondents to a short web survey on smoking, discrimination, and health. In the nomination condition after completing the survey both LGBT and non-LGBT seeds were invited to share the names and email address of up to four LGBT persons they knew. In the recruitment condition, seeds were given four unique PINs and links to the survey to distribute to LGBT persons. Both conditions were successful in producing new LGBT respondents. The recruitment condition was much more productive. LGBT seeds (and their recruits) were much connected to and willing to contact other LGBT people they knew to participate in a survey. Comparisons of characteristics and responses from the initial samples and the LGBT referrals as well as comparisons to LGB samples from a large national survey are presented. Results demonstrate the promise of this hybrid technique for increasing the number of LGBT respondents through referrals from an initial probability based sample. [ABSTRACT FROM AUTHOR]

Information spreading processes are main drivers of viral campaigns. They are usually conducted within large scale social networks. Parametrisation of online campaigns is usually related to allocation of budgets, number of seeds and strategies of their selection. It is hard to predict campaign effects. Proposed in this paper approach uses network samples to select appropriate strategy for use within complete network. Results showed how scaling of samples is affecting approximation quality. Multi-criteria analysis of performance allows for strategy selection according to preferences and goals. [ABSTRACT FROM AUTHOR]

The temporal dynamics of plant phenology and pollinator abundance across seasons should influence the structure of plant–pollinator interaction networks. Nevertheless, such dynamics are seldom considered, especially for diverse tropical networks.Here, we evaluated the temporal variation of four plant–pollinator networks in two seasonal ecosystems in Central Brazil (Cerrado and Pantanal). Data were gathered on a monthly basis over 1 year for each network. We characterized seasonal and temporal shifts in plant–pollinator interactions, using temporally discrete networks. We predicted that the greater floral availability in the rainy season would allow for finer partitioning of the floral niche by the pollinators, i.e. higher specialization patterns as previously described across large spatial gradients. Finally, we also evaluated how sampling restricted to peak flowering period may affect the characterization of the networks.Contrary to our expectations, we found that dry season networks, although characterized by lower floral resource richness and abundance, showed higher levels of network‐wide interaction partitioning (complementary specialization and modularity). For nestedness, though, this between‐seasons difference was not consistent. Reduced resource availability in the dry season may promote higher interspecific competition among pollinators leading to reduced niche overlap, thus explaining the increase in specialization.There were no consistent differences between seasons in species‐level indices, indicating that higher network level specialization is an emergent property only seen when considering the entire network. However, bees presented higher values of specialization and species strength in relation to other groups such as flies and wasps, suggesting that some plant species frequently associated with bees are used only by this group.Our study also indicates that targeted data collection during peak flowering generates higher estimates of network specialization, possibly because species activity spans longer periods than the targeted time frame. Hence, depending on the period of data collection, different structural values for the networks of interactions may be found.Synthesis. Plant–pollinator networks from tropical environments have structural properties that vary according to seasons, which should be taken into account in the description of the complex systems of interactions between plants and their pollinators in these areas. Plant–pollinator networks from tropical environments have structural properties that vary according to seasons, which should be taken into account in the description of the complex systems of interactions between plants and their pollinators in these areas. [ABSTRACT FROM AUTHOR]

In this article, we propose a general model of data collection from social media, in the context of terrorism research, focusing on recent studies of jihadists. By analyzing Twitter data collection methods in the existing research, we show that the methods used are prone to sampling biases, and that the sampled datasets are not sufficiently filtered or validated to ensure reliability of conclusions derived from them. Alternatively, we propose some best practices for the collection of data in future research on jihadist using social media (as well as other kinds of terrorist groups). Given the similarity of the methodological challenges posed by research on almost all social media platforms, in the context of terrorism studies, the critique and recommendations offered remain relevant despite the recent shift of most jihadists from Twitter to Telegram and other forms of social media. [ABSTRACT FROM AUTHOR]

Social activity networks are formed from activities among users (such as wall posts, tweets, emails, and etc.), where any activity between two users results in an addition of an edge to the network graph. These networks are streaming and include massive volume of edges. A streaming graph is considered to be a stream of edges that continuously evolves over time. This paper proposes a sampling algorithm for social activity networks, implemented in a streaming fashion. The proposed algorithm utilizes a set of fixed structure learning automata. Each node of the original activity graph is equipped with a learning automaton which decides whether its corresponding node should be added to the sample set or not. The proposed algorithm is compared with the best streaming sampling algorithm reported so far in terms of Kolmogorov-Smirnov (KS) test and normalized L1 and L2 distances over real-world activity networks and synthetic networks presented as a sequence of edges. The experimental results show the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Respondent-driven sampling (RDS) is a link-tracing procedure used in epidemiologic research on hidden or hard-to-reach populations in which subjects recruit others via their social networks. Estimates from RDS studies may have poor statistical properties due to statistical dependence in sampled subjects' traits. Two distinct mechanisms account for dependence in an RDS study: homophily, the tendency for individuals to share social ties with others exhibiting similar characteristics, and preferential recruitment, in which recruiters do not recruit uniformly at random from their network alters. The different effects of network homophily and preferential recruitment in RDS studies have been a source of confusion and controversy in methodological and empirical research in epidemiology. In this work, we gave formal definitions of homophily and preferential recruitment and showed that neither is identified in typical RDS studies. We derived nonparametric identification regions for homophily and preferential recruitment and showed that these parameters were not identified unless the network took a degenerate form. The results indicated that claims of homophily or recruitment bias measured from empirical RDS studies may not be credible. We applied our identification results to a study involving both a network census and RDS on a population of injection drug users in Hartford, Connecticut (2012-2013). [ABSTRACT FROM AUTHOR]

Since online social networks usually have quite huge size and limited access, smaller subgraphs of them are often produced and analysed as the representative samples of original graphs. Sampling algorithms proposed so far are categorized into three main classes: node sampling, edge sampling, and topology-based sampling. Classic node sampling algorithm, despite its simplicity, performs surprisingly well in many situations. But the problem with node sampling is that the connectivity in sampled subgraph is less likely to be preserved. This paper proposes a topology–based node sampling algorithm using irregular cellular learning automata (ICLA), called ICLA-NS. In this algorithm, at first an initial sample subgraph of the input graph is generated using the node sampling method and then an ICLA isomorphic to the input graph is utilized to improve the sample in such a way that the connectivity of the sample is ensured and at the same time the high degree nodes are also included in the sample. Experimental results on real–world social networks indicate that the proposed sampling algorithm ICLA-NS preserves more accurately the underlying properties of the original graph compared to existing sampling methods in terms of Kolmogorov-Smirnov (KS) test. [ABSTRACT FROM AUTHOR]

Although much research has been devoted to unbiased sampling of various networks, bias is not always disadvantageous, but sometimes useful. Especially for many real-world applications such as detecting influential nodes, spam users, and the most trustful people, it is preferred to sample users with special properties. Since sampling from friendship network alone cannot collect these important nodes appropriately, one may use interactions occurred among users. This paper deals with biased sampling of multilayer activity network. The proposed method initially learns the transition probabilities according to the considered application using learning automata. Then we sample the graph by running an application-based random walk following the learnt probabilities, in order to be guided to suitable nodes and collect their information. At last, the performance of the proposed method in terms of different applications such as fame, spam, and trust is evaluated and compared with those of common sampling algorithms. According to the experiments done, biased sampling method based on learning automata outperforms all other sampling approaches including simple random walk, Metropolis-Hastings random walk, BFS, forest fire, degree, and uniform sampling in terms of all the evaluation measures. To the best of our knowledge, our method is the first and only biased sampling method which can be used in a multilayer activity network. [ABSTRACT FROM AUTHOR]

Cluster sampling with multiplicity uses the concept of counting rule of multiplicity in order to include in the survey those individuals not belonging to the sample. Additionally, some results to improve the efficiency and for the variance components from multiplicity estimators of the population total are derived. Finally, a simulation exercise to illustrate the magnitude of the gain in the efficiency with the sampling with multiplicity in function of the sample size and the extent of the counting rule is presented.El muestreo de conglomerados con multiplicidad utiliza el concepto de regla de conteo de multiplicidad para incluir en la encuesta individuos no pertenecientes a la muestra. Se derivan las fórmulas para la ganancia de eficiencia y para los componentes de varianza de dos estimadores de multiplicidad del total poblacional. Mediante simulación se ilustra la magnitud de la ganancia de eficiencia con el muestreo con multiplicidad en función del tamaño de muestra y la amplitud de la regla de conteo.

Link-tracing designs are often used to estimate the size of hidden populations by utilizing the relational links between their members. A major problem in studies of hidden populations is the lack of a convenient sampling frame. The most frequently applied design in studies of hidden populations is respondent-driven sampling in which no sampling frame is used. However, in some studies multiple but incomplete sampling frames are available. In this article, we introduce the B-graph design that can be used in such situations. In this design, all available incomplete sampling frames are joined and turned into one sampling frame, from which a random sample is drawn and selected respondents are asked to mention their contacts. By considering the population as a bipartite graph of a two-mode network (those from the sampling frame and those who are not on the frame), the number of respondents who are directly linked to the sampling frame members can be estimated using Chao's and Zelterman's estimators for sparse data. The B-graph sampling design is illustrated using the data of a social network study from Utrecht, the Netherlands. [ABSTRACT FROM AUTHOR]

Randomized graph sampling (RGS) is an approach for sampling populations associated with or describable as graphs, when the structure of the graph is known and the parameter of interest is the total weight of the graph. RGS is related to, but distinct from, other graph-based approaches such as snowball and network sampling. Graph elements are clustered into walks that reflect the structure of the graph, as well as operational constraints on sampling. The basic estimator in RGS can be constructed as a Horvitz-Thompson estimator. I prove it to be design-unbiased, and also show design-unbiasedness of an estimator of the sample variance when walks are sampled with replacement. Covariates can be employed for variance reduction either through improved assignment of selection probabilities to walks in the design step, or through the use of alternative estimators during analysis. The approach is illustrated with a trail maintenance example, which demonstrates that complicated approaches to assignment of selection probabilities can be counterproductive. I describe conditions under which RGS may be efficient in practice, and suggest possible applications. [ABSTRACT FROM AUTHOR]

One of the many challenges hindering the global response to the human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) epidemic is the difficulty of collecting reliable information about the populations most at risk for the disease. Thus, the authors empirically assessed a promising new method for estimating the sizes of most at-risk populations: the network scale-up method. Using 4 different data sources, 2 of which were from other researchers, the authors produced 5 estimates of the number of heavy drug users in Curitiba, Brazil. The authors found that the network scale-up and generalized network scale-up estimators produced estimates 5–10 times higher than estimates made using standard methods (the multiplier method and the direct estimation method using data from 2004 and 2010). Given that equally plausible methods produced such a wide range of results, the authors recommend that additional studies be undertaken to compare estimates based on the scale-up method with those made using other methods. If scale-up-based methods routinely produce higher estimates, this would suggest that scale-up-based methods are inappropriate for populations most at risk of HIV/AIDS or that standard methods may tend to underestimate the sizes of these populations. [ABSTRACT FROM PUBLISHER]

Ecologists increasingly use network theory to examine animal association patterns. The gambit of the group (GoG) is a simple and useful assumption for accumulating the data necessary for a network analysis. The gambit of the group implies that each animal in a group is associating with every other individual in that group. Sampling is an important issue for networks in wild populations collected assuming GoG. Due to time, effort, and resource constraints and the difficulty of tracking animals, sampled data are usually a subset of the actual network. Ecologists often use association indexes to calculate the frequency of associations between individuals. These indexes are often transformed by applying a filter to produce a binary network. We explore GoG sampling using model networks. We examine assortment at the level of the group by a single dichotomous trait, along with many other network measures, to examine the effect of different sampling regimes, and choice of filter on the accuracy and precision with which measures are estimated. We find strong support for the use of weighted, rather than filtered, network measures and show that different filters have different effects depending on the nature of the sampling. We make several practical recommendations for ecologists planning GoG sampling. [ABSTRACT FROM AUTHOR]

After the completion of the human and other genome projects it emerged that the number of genes in organisms as diverse as fruit flies, nematodes, and humans does not reflect our perception of their relative complexity. Here, we provide reliable evidence that the size of protein interaction networks in different organisms appears to correlate much better with their apparent biological complexity. We develop a stable and powerful, yet simple, statistical procedure to estimate the size of the whole network from subnet data. This approach is then applied to a range of eukaryotic organisms for which extensive protein interaction data have been collected and we estimate the number of interactions in humans to be ≈650,000. We find that the human interaction network is one order of magnitude bigger than the Drosophila melanogaster interactome and ≈3 times bigger than in Caenorhabditis elegans. [ABSTRACT FROM AUTHOR]

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A flexible class of adaptive sampling designs is introduced for sampling in network and spatial settings. In the designs, selections are made sequentially with a mixture distribution based on an active set that changes as the sampling progresses, using network or spatial relationships as well as sample values. The new designs have certain advantages compared with previously existing adaptive and link-tracing designs, including control over sample sizes and of the proportion of effort allocated to adaptive selections. Efficient inference involves averaging over sample paths consistent with the minimal sufficient statistic. A Markov chain resampling method makes the inference computationally feasible. The designs are evaluated in network and spatial settings using two empirical populations: a hidden human population at high risk for HIV/AIDS and an unevenly distributed bird population. [ABSTRACT FROM AUTHOR]