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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.

Successive sampling population size estimation (SS-PSE) is a method used by government agencies, aid organizations, and researchers around the world to estimate the size of hidden populations using data from respondent-driven sampling surveys. SS-PSE addresses a specific need in estimation, since many countries rely on having accurate size estimates to plan and allocate finite resources to address the needs of hidden populations. However, SS-PSE relies on several assumptions, one of which requires the underlying social network of the hidden population to be fully connected. We propose two modifications to SS-PSE for estimating the size of hidden populations whose underlying social network is composed of disjoint clusters. The first method is a theoretically straightforward extension of SS-PSE, but it relies on prior information that may be difficult to obtain in practice. The second method extends the Bayesian SS-PSE model by introducing a new set of parameters that allow for clustered estimation without requiring the additional prior information. After providing theoretical justification for both novel methods, we then assess their performance using simulations and apply the Clustered SS-PSE method to a population of internally displaced persons in Bamako, Mali. [ABSTRACT FROM AUTHOR]

In this paper, we focus on respondent-driven sampling (RDS), which is a valuable survey methodology to estimate the size and the characteristics of hidden or hard-to-measure population groups. The RDS methodology makes it possible to gather information on these populations by exploiting the relationships between their components. However, RDS suffers from the lack of an estimation methodology that is sufficiently robust to accommodate the varying conditions under which it is applied. In this paper, we address the estimation problem of the RDS methodology and, by approaching it as a particular indirect sampling technique, we propose three unbiased estimation methods as possible solutions. [ABSTRACT FROM AUTHOR]

Familial or family aggregation of a disease is important for studying possible genetic etiology of a disease. A popular and useful measure of family aggregation is recurrence risk. Household health surveys with (family) network sampling, which surveyed individuals report about disease status of themselves and specified relatives, have been shown to be useful for estimating prevalence of diseases and more recently for estimating recurrence risk of disease using nonparametric classical survey methods. Because these surveys have complex sample designs with sample weighting for differential sample selection rates, this paper extends the composite-likelihood estimation and hypothesis of parameters of the quadratic exponential model (QEM) for simple random samples to data from these complex sample designs. In addition, the QEM is extended to simultaneously estimate and test parameters and recurrence risk for multiple family relationships, for comparing recurrence risk across family-level covariates (e.g. race) and utilizing propensity score weighting to adjust for confounding by individual-level covariates (e.g. age). Simulations are used to study the finite sample properties of the parameter estimation, variance estimation and level and power of hypothesis testing based on derived Wald and Quasi-Score tests for these extended QEMs. Finally, our methods are illustrated using the 1976 National Health Interview Survey diabetes data set. [ABSTRACT FROM AUTHOR]

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.

We consider incomplete observations of stochastic processes governing the spread of infectious diseases through finite populations by way of contact. We propose a flexible semiparametric modelling framework with at least three advantages. First, it enables researchers to study the structure of a population contact network and its impact on the spread of infectious diseases. Second, it can accommodate short- and long-tailed degree distributions and detect potential superspreaders, who represent an important public health concern. Third, it addresses the important issue of incomplete data. Starting from first principles, we show when the incomplete-data generating process is ignorable for the purpose of Bayesian inference for the parameters of the population model. We demonstrate the semiparametric modelling framework by simulations and an application to the partially observed MERS epidemic in South Korea in 2015. We conclude with an extended discussion of open questions and directions for future research. [ABSTRACT FROM AUTHOR]

• Assessment of implementing two network research studies in conflict-affected DRC. • Negotiating access to field sites and respondents in trust-sensitive contexts. • Mixed methods approaches to social network data collection and analysis. • Importance of trust for collecting quality data in unstable environments. Data collection in social network research has advanced to include online questionnaires, digital metadata mining of internet sites, and the use of remote-sensing technologies. Some scholars however call for more attention to nuanced understandings of ties and contexts in studies of social structure and relationships, evoking practices that characterise the field's foundational works. This article's two studies reference these earlier efforts, drawing on ethnography and primary data collection. Both were undertaken in conflict-affected eastern Democratic Republic of the Congo (DRC) and broadly aimed to refine understandings of public authority and governance. Such research strives to inform humanitarian interventions to support social structures and actors which benefit their communities – however unexpected and unconventional. The first study (2016) employed a novel link-tracing design to examine personal support networks entwining purportedly hostile sub-populations, from combatants to unaffiliated civilians. The second (2018−20) focussed on access to essential social services across different governance arrangements, areas dominated by tenuous alliances of domestic or foreign militias and other actors. Leveraging an egocentric network design, it yielded multilevel relational network chain data. Each study was rife with obstacles related to accessing participants, sampling, reliability, and validity. We reflect on this network collection experience, foregrounding the interdependence between trust and data quality brought into stark relief by the setting's instability and insecurity. This interdependency impacts all social network research, especially when it involves precarious contexts or sensitive topics. [ABSTRACT FROM AUTHOR]

• Diagnostics of respondent-driven sampling (RDS) should use rolling values. • Diagnostics with geographical data can inform RDS process. • Convex hulls provide a measure of RDS reach. • Rolling convex hulls show when RDS might get stuck. Respondent-driven sampling (RDS) is commonly used to sample from key populations without a sampling frame since traditional methods are unable to efficiently survey them. Surveying these populations is often desirable to inform service delivery, assess effectiveness of programs, and determine prevalence of diseases. However, there are concerns about how RDS works in practice due to its many assumptions. To assess some of these assumptions, we develop diagnostics using geographical data and demonstrate their utility by identifying lack of convergence and characterizing RDS reach in surveys conducted among female sex workers and men who have sex with men in Kampala, Uganda. [ABSTRACT FROM AUTHOR]

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]

• Assessment of implementing two network research studies in conflict-affected DRC. • Negotiating access to field sites and respondents in trust-sensitive contexts. • Mixed methods approaches to social network data collection and analysis. • Importance of trust for collecting quality data in unstable environments. Data collection in social network research has advanced to include online questionnaires, digital metadata mining of internet sites, and the use of remote-sensing technologies. Some scholars however call for more attention to nuanced understandings of ties and contexts in studies of social structure and relationships, evoking practices that characterise the field's foundational works. This article's two studies reference these earlier efforts, drawing on ethnography and primary data collection. Both were undertaken in conflict-affected eastern Democratic Republic of the Congo (DRC) and broadly aimed to refine understandings of public authority and governance. Such research strives to inform humanitarian interventions to support social structures and actors which benefit their communities – however unexpected and unconventional. The first study (2016) employed a novel link-tracing design to examine personal support networks entwining purportedly hostile sub-populations, from combatants to unaffiliated civilians. The second (2018−20) focussed on access to essential social services across different governance arrangements, areas dominated by tenuous alliances of domestic or foreign militias and other actors. Leveraging an egocentric network design, it yielded multilevel relational network chain data. Each study was rife with obstacles related to accessing participants, sampling, reliability, and validity. We reflect on this network collection experience, foregrounding the interdependence between trust and data quality brought into stark relief by the setting's instability and insecurity. This interdependency impacts all social network research, especially when it involves precarious contexts or sensitive topics. [ABSTRACT FROM AUTHOR]

• We examine the effectiveness of imputation methods for missing network data. • We evaluate imputation methods under different missing data conditions and measures. • Simple reconstruction approaches often perform as well as model-based approaches. • The optimal imputation method varies by measure of interest and network type. • Researchers can use our results as a guide to making imputation decisions. Missing data is a common, difficult problem for network studies. Unfortunately, there are few clear guidelines about what a researcher should do when faced with incomplete information. We take up this problem in the third paper of a three-paper series on missing network data. Here, we compare the performance of different imputation methods across a wide range of circumstances characterized in terms of measures, networks and missing data types. We consider a number of imputation methods, going from simple imputation to more complex model-based approaches. Overall, we find that listwise deletion is almost always the worst option, while choosing the best strategy can be difficult, as it depends on the type of missing data, the type of network and the measure of interest. We end the paper by offering a set of practical outputs that researchers can use to identify the best imputation choice for their particular research setting. [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]

Estimating the prevalence of sex trafficking requires a practical sampling strategy to reach the hidden population. In this study, we experimented with a network sampling design to obtain a sample of sex workers from the city of Muzaffarpur, India. Backed by census data and other auxiliary information, we obtained a stratified initial sample of 111 individuals and with two waves of referrals arrived at a final sample of 317 individuals. A sophisticated network-based approach is used to estimate the population size, and a respondent-driven sampling–based strategy is used to estimate characteristics related to sex trafficking violations. We detail the sampling design and present results from the study, highlighting significant findings and lessons learned that can be used for future studies. [ABSTRACT FROM AUTHOR]

Social networks analysis (SNA) has been prevalent in the research community for decades. The challenges of SNA study include the massive quantity and often incomplete availability of the network. Therefore, researchers have to estimate and/or predict the behavior, structure and topology of the network using sampling techniques. In this way, the trends and probable patterns of the massive network are predicted or identified. The existing sampling techniques, e.g., topology-based sampling, random walk sampling and random selection sampling, have critical issues on the performance on representativeness and consistent over different networks. In this paper, an efficient hybrid evolutionary sampling algorithm named GA-CS is presented for large-scale networks. Based on three measures of degree, clustering coefficient, and betweenness centrality of the nodes of the network, the proposed algorithm is compared with classical network sampling methods (BFS, SRW, MHRW, SBS, FF, RN and RE). The quality of the sampled data is assessed based on Kolmogorov–Smirnov D statistics, normalized mean square error (NMSE) and Friedman's test. According to the results, the generated samples using the proposed sampling algorithm are more similar to the original networks compared to the other sampling methods; also, the representativeness and consistency of the proposed algorithm are high over different large-scale networks. [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.

This paper addresses the challenge of determining community scale to which network nodes belong and introduces an innovative hypothesis testing approach. It begins with a network sampling method that generates sequences of node dependency values, revealing community structure and scale in a waveform-like manner. Subsequently, the study employs wavelet analysis, a signal processing technique, to extract local signal periodicity information from these sequences. This information is then used to develop a test for assessing node membership in specific community scales. The proposed method is applied to both simulated and real-world social network data, with results from the simulated data demonstrating its effectiveness in evaluating node membership in particular community scales. [ABSTRACT FROM AUTHOR]

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.

Visualization strategies facilitate streaming network analysis by allowing its exploration through graphical and interactive layouts. Depending on the strategy and the network density, such layouts may suffer from a high level of visual clutter that hides meaningful temporal patterns, highly active groups of nodes, bursts of activity, and other important network properties. Edge sampling improves layout readability, highlighting important properties and leading to easier and faster pattern identification and decision making. This paper presents Streaming Edge Sampling for Network Visualization–SEVis, a streaming edge sampling method that discards edges of low-active nodes while preserving a distribution of edge counts that is similar to the original network. It can be applied to a variety of layouts to enhance streaming network analyses. We evaluated SEVis performance using synthetic and real-world networks through quantitative and visual analyses. The results indicate a higher performance of SEVis for clutter reduction and pattern identification when compared with other sampling methods. [ABSTRACT FROM AUTHOR]

• 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.

Network Embedding (NE) has emerged as a powerful tool in many applications. Many real-world networks have multiple types of relations between the same entities, which are appropriate to be modeled as multiplex networks. However, at random walk-based embedding study for multiplex networks, very little attention has been paid to the problems of sampling bias and imbalanced relation types. In this paper, we propose an Adaptive Node Embedding Framework (ANEF) based on cross-layer sampling strategies of nodes for multiplex networks. ANEF is the first framework to focus on the bias issue of sampling strategies. Through metropolis hastings random walk (MHRW) and forest fire sampling (FFS), ANEF is less likely to be trapped in local structure with high degree nodes. We utilize a fixed-length queue to record previously visited layers, which can balance the edge distribution over different layers in sampled node sequence processes. In addition, to adaptively sample the cross-layer context of nodes, we also propose a node metric called Neighbors Partition Coefficient (NPC). Experiments on real-world networks in diverse fields show that our framework outperforms the state-of-the-art methods in application tasks such as cross-domain link prediction and mutual community detection. [ABSTRACT FROM AUTHOR]

In this article, we propose a new method to perform topological network sampling. Topological network sampling is a process for extracting a subset of nodes and edges from a network, such that analyses on the sample provide results and conclusions comparable to the ones they would return if run on whole structure. We need network sampling because the largest online network datasets are accessed through low-throughput application programming interface (API) systems, rendering the collection of the whole network infeasible. Our method is inspired by the literature on network backboning, specifically the noise-corrected backbone. We select the next node to explore by following the edge we identify as the one providing the largest information gain, given the topology of the sample explored so far. We evaluate our method against the most commonly used sampling methods. We do so in a realistic framework, considering a wide array of network topologies, network analysis, and features of API systems. There is no method that can provide the best sample in all possible scenarios, thus in our results section, we show the cases in which our method performs best and the cases in which it performs worst. Overall, the noise-corrected network sampling performs well: it has the best rank average among the tested methods across a wide range of applications. [ABSTRACT FROM AUTHOR]

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.

Despite the well-known dependence of vertex and network structural parameters on network boundary specification employed by researchers, there has so far been effectively no discussion of this methodological caveat in the global and world city literature. Given the reliance of empirical studies of urban networks on the sampling of underlying actors that form these networks by their interactions, we consider it of key importance to examine the dependence of network centralities of cities on network boundary specification. We consider three distinctive modelling approaches based on: (a) office networks, (b) ownership ties and (c) inter-organisational projects. Our results indicate that city network centralities obtained from sampled networks are highly consistent with those obtained from whole network analysis for samples featuring as little as 4% (office networks), 10% (ownership ties) and 25% (inter-organisational projects) of the underlying actors. [ABSTRACT FROM AUTHOR]

• Bias from respondent-driven samples derives mainly from differences in respondent degree, and differential recruitment. • Two different ways of analytically decomposing bias into a degree component (DC) and a recruitment component (RC) are shown. • Simulated RDS samples from empirical networks show that estimates of DC and RC can predict which RDS estimators perform best. • A key implication is that data from the sample itself can be used for RDS estimator selection. Respondent-Driven Sampling (RDS) is a method of network sampling that is used to sample hard-to-reach populations. The resultant sample is non-random, but different weighting methods can account for the over-sampling of (1) high-degree individuals and (2) homophilous groups that recruit members more effectively. While accounting for degree-bias is almost universally agreed upon, accounting for recruitment-bias has been debated as it can further increase estimate variance without substantially reducing bias. Simulation-based research has examined which weighting procedures perform best given underlying population network structures, group recruitment differences, and sampling processes. Yet, in the field, analysts do not have a priori knowledge of the network they are sampling. We show that the RDS sample data itself can determine whether a degree-based estimator is sufficient. Formulas derived from the decomposition of a 'dual-component' estimator can approximate the 'recruitment component' (RC) and 'degree component' (DC) of a sample's bias. Simulations show that RC and DC values can predict the performance of different classes of estimators. Samples with extreme 'RC' values, a consequence of network homophily and differential recruitment, are better served by a classical estimator. The use of sample data to improve estimator selection is a promising innovation for RDS, as the population network features that should guide estimator selection are typically unknown. [ABSTRACT FROM AUTHOR]

Agent-based modeling holds great potential as an analytical tool. Agent-based models (ABMs) are, however, also vulnerable to critique, as they often employ stylized social worlds, with little connection to the actual environment in question. Given these concerns, there has been a recent call to more fully incorporate empirical data into ABMs. This article falls in this tradition, exploring the benefits of using sampled ego network data in ABMs of cultural diffusion. Thus, instead of relying on full network data, which can be difficult and costly to collect, or no empirical network data, which is convenient but not empirically grounded, we offer a middle-ground, one combining ABMs with recent work on network sampling. The main question is whether this approach is effective. We provide a test of the approach using six complete networks; the test also includes a range of diffusion models (where actors follow different rules of adoption). For each network, we take a random ego network sample and use that sample to infer the full network structure. We then run a diffusion model through the known, complete networks, as well as the inferred networks, and compare the results. The results, on the whole, are quite strong: Across all analyses, the diffusion curves based on the sampled data are very similar to the curves based on the true, complete network. This suggests that ego network sampling can, in fact, offer a practical means of incorporating empirical data into an agent-based model. [ABSTRACT FROM AUTHOR]

Network concepts are often used to characterize the features of a social context. For example, past work has asked if individuals in more socially cohesive neighborhoods have better mental health outcomes. Despite the ubiquity of use, it is relatively rare for contextual studies to use the methods of network analysis. This is the case, in part, because network data are difficult to collect, requiring information on all ties between all actors. In this article the authors ask whether it is possible to avoid such heavy data collection while still retaining the best features of a contextual-network study. The basic idea is to apply network sampling to the problem of contextual models, in which one uses sampled ego network data to infer the network features of each context and then uses the inferred network features as second-level predictors in a hierarchical linear model. The authors test the validity of this idea in the case of network cohesion. Using two complete data sets as a test, the authors find that ego network data are sufficient to capture the relationship between cohesion and important outcomes, such as attachment and deviance. The hope, going forward, is that researchers will find it easier to incorporate holistic network measures into traditional regression models. [ABSTRACT FROM AUTHOR]

There is a tendency to consider covert networks as separate from overt networks. Drawing on data from the Democratic Republic of the Congo, we demonstrate that this is not the case and identify how covert and overt networks are mutually constitutive. While most studies of African brokers have relied on network metaphors like 'Big Men' and 'social membranes', we consider the embeddedness of 'covert' networks in 'overt' networks explicitly. We perform two analyses on a large original dataset encompassing 396 partially overlapping ego-nets obtained from a hybrid link-tracing design. An ego-net analysis reveals a large degree of homophily and a deep embeddedness of the different networks. A multilevel exponential random graph model fitted to the reconstructed network of a 110-node subset shows that demobilised combatants are the actors likely to broker between armed groups, state forces, and civilian blocs, suggesting their capacity to broker peace or foment war. [ABSTRACT FROM AUTHOR]

Summary: The paper provides statistical theory and intuition for personalized PageRank (called 'PPR'): a popular technique that samples a small community from a massive network. We study a setting where the entire network is expensive to obtain thoroughly or to maintain, but we can start from a seed node of interest and 'crawl' the network to find other nodes through their connections. By crawling the graph in a designed way, the PPR vector can be approximated without querying the entire massive graph, making it an alternative to snowball sampling. Using the degree‐corrected stochastic block model, we study whether the PPR vector can select nodes that belong to the same block as the seed node. We provide a simple and interpretable form for the PPR vector, highlighting its biases towards high degree nodes outside the target block. We examine a simple adjustment based on node degrees and establish consistency results for PPR clustering that allows for directed graphs. These results are enabled by recent technical advances showing the elementwise convergence of eigenvectors. We illustrate the method with the massive Twitter friendship graph, which we crawl by using the Twitter application programming interface. We find that the adjusted and unadjusted PPR techniques are complementary approaches, where the adjustment makes the results particularly localized around the seed node, and that the bias adjustment greatly benefits from degree regularization. [ABSTRACT FROM AUTHOR]

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]

Sampling random graphs is essential in many applications, and often algorithms use Markov chain Monte Carlo methods to sample uniformly from the space of graphs. However, often there is a need to sample graphs with some property that we are unable, or it is too inefficient, to sample using standard approaches. In this article, we are interested in sampling graphs from a conditional ensemble of the underlying graph model. We present an algorithm to generate samples from an ensemble of connected random graphs using a Metropolis–Hastings framework. The algorithm extends to a general framework for sampling from a known distribution of graphs, conditioned on a desired property. We demonstrate the method to generate connected spatially embedded random graphs, specifically the well-known Waxman network, and illustrate the convergence and practicalities of the algorithm. [ABSTRACT FROM AUTHOR]

Summary: People who inject drugs are an important population to study to reduce transmission of blood‐borne illnesses including human immunodeficiency virus and hepatitis. We estimate the human immunodeficiency virus and hepatitis C prevalence among people who inject drugs in Mauritius. Respondent‐driven sampling (RDS), which is a widely adopted link tracing sampling design used to collect samples from hard‐to‐reach human populations, was used to collect this sample. The random‐walk approximation underlying many common RDS estimators assumes that each social relationship (edge) in the underlying social network has an equal probability of being traced in the collection of the sample. This assumption does not hold in practice. We show that certain RDS estimators are sensitive to the violation of this assumption. To address this limitation in current methodology, and the effect that it may have on prevalence estimates, we present a new method for improving RDS prevalence estimators using estimated edge inclusion probabilities, and we apply this to data from Mauritius. [ABSTRACT FROM AUTHOR]