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In this paper we compare two methods for estimating the size of personal networks using a nationally representative sample of the United States. Both methods rely on the ability of respondents to estimate the number of people they know in specific subpopulations of the U.S. (e.g., diabetics, Native Americans) and people in particular relation categories (e.g., immediate family, coworkers). The results demonstrate a remarkable similarity between the average network size generated by both methods (approximately 291). Similar results were obtained with a separate national sample. An attempt to corroborate our estimates by replication among a population we suspect has large networks (clergy), yielded a larger average network size.Extensive investigation into the existence of response effects showed some preference for using certain numbers when making estimates, but nothing that would significantly affect the estimate of network size beyond about 6 percent. We conclude that both methods for estimating personal network size yield valid and reliable proxies for actual network size, but questions about accuracy remain.

Resumen En este artículo comparamos dos métodos para la estimación del tamaño de las redes personales utilizando una muestra representativa de Estados Unidos a nivel nacional. Ambos métodos se basan en la habilidad de las personas encuestadas para estimar el número de personas que conocen en subpoblaciones específicas de EE.UU. (ej.: diabéticos, nativo-americanos) y gente en categorías específicas de relación (ej.: familia inmediata, compañeros de trabajo). Los resultados muestran una remarcable similitud entre el tamaño medio de la red obtenido por ambos métodos (aproximadamente 291). Se obtuvieron resultados similares con una muestra nacional distinta. La tentativa de corroboración de nuestras estimaciones mediante una reproducción exacta de la encuesta entre un segmento de población propenso a tener redes más amplias (el clero), dio como resultado un tamaño medio de la red superior. Una investigación extensiva sobre la existencia de efectos de respuesta mostró algunas preferencias por usar ciertos números a la hora de realizar estimaciones, pero nada que afectase de forma significativa a la estimación de tamaño de la red más allá del 6 por ciento. Nuestra conclusión es que ambos métodos utilizados para la estimación del tamaño de las redes personales proporcionan resultados válidos y fiables del tamaño de la red real, pero quedan algunas cuestiones pendientes sobre la exactitud. Abstract In this paper we compare two methods for estimating the size of personal networks using a nationally representative sample of the United States. Both methods rely on the ability of respondents to estimate the number of people they know in specific subpopulations of the U.S. (e.g., diabetics, Native Americans) and people in particular relation categories (e.g., immediate family, coworkers). The results demonstrate a remarkable similarity between the average network size generated by both methods (approximately 291). Similar results were obtained with a separate national sample. An attempt to corroborate our estimates by replication among a population we suspect has large networks (clergy), yielded a larger average network size. Extensive investigation into the existence of response effects showed some preference for using certain numbers when making estimates, but nothing that would significantly affect the estimate of network size beyond about 6 percent. We conclude that both methods for estimating personal network size yield valid and reliable proxies for actual network size, but questions about accuracy remain.

We examine methods for reducing respondent burden in evaluating alter–alter ties on a set of network structural measures. The data consist of two sets, each containing 45 alters from respondent free lists: the first contains 447 personal networks, and the second 554. Respondents evaluated the communication between 990 alter pairs. The methods were (1) dropping alters from the end of the free-list, (2) randomly dropping alters, (3) randomly dropping links, and (4) predicting ties based on transitivity. For some measures network structure is captured with samples of less than 20 alters; other measures are less consistent. Researchers should be aware of the need to sample a minimum number of alters to capture structural variation. [Copyright &y& Elsevier]

Abstract: We analyse 10,920 shortest path connections between 105 members of an interviewing bureau, together with the equivalent conceptual, or ‘small world’ routes, which use individuals’ selections of intermediaries. This permits the first study of the impact of accuracy within small world chains. The mean small world path length (3.23) is 40% longer than the mean of the actual shortest paths (2.30), showing that mistakes are prevalent. A Markov model with a probability of simply guessing an intermediary of 0.52 gives an excellent fit to the observations, suggesting that people make the wrong small world choice more than half the time. [Copyright &y& Elsevier]

We asked respondents how many people they knew in many subpopulations. These numbers, averaged over large representative samples. should vary proportionally to the size of the subpopulations. In fact, they do not. We give two different interpretations of this finding. The first interpretation notes that the responses are linear in subpopulation size for small subpopulations, but with a non-zero off-set, and become noisier for larger subpopulations. Our explanation assumes that respondents both invent and forget members of their networks in the subpopulations. in addition to guessing when the number concerned becomes large. The second interpretation notes that the responses are well described by a power law response, in which the mean number of subpopulation members reported known varies as the square root of the subpopulation size. Despite the apparent implausibility of this, we suggest a psychological mechanism and a model which is able to reproduce the behaviour. Other recall data are shown to have similar properties, thus widening the relevance of the findings. [ABSTRACT FROM AUTHOR]

Results from a representative survey of respondents in Florida are given, concerning their knowledge about members of their personal network, and specifically how many people respondents know in selected subpopulations. We employ a method known as a "network scale-up method". By using a collection of subpopulations of known size, and also asking about one subpopulation (those who are seropositive) of unknown size, we make various estimates of personal network size and the size of the seropositive subpopulation. Our best (maximum likelihood, unbiased) estimates are 108 members of the network defined by "having been in contact with during the previous two years", and (approximately unbiased) 1.6 million for the seropositive subpopulation. Because of the proportional over-representation of AIDS (and presumably, therefore, seropositive) in Florida, by a factor of about two, this latter estimate could be an overestimate. [ABSTRACT FROM AUTHOR]

In this paper we introduce and evaluate a method for eliciting a representative sample of total personal networks. First names were used as a cue to elicit a sample of 14 alters from 712 respondents through a telephone interview. Network characteristics for each respondent were calculated as averages and proportions across the 14 alters. These were compared to other studies using more specialized network generators. Our method produced results which are logically consistent with those expected from a generator that elicits a sample from the total rather than a specialized subset of the total network. The proportions of kin relations, average tie strength and frequency of contacts are found to be lower than network generators designed to elicit networks of social support. Given our conclusion that the sample is representative of the total network, we examine the varying characteristics of respondents and their networks based on the domination of a particular relation type in their network. This analysis provides answers to such questions as "What characteristics of respondents account for the proportion of family relations in their network?' and 'What are the similarities between respondents whose networks are made up of mostly work-related relations?' [ABSTRACT FROM AUTHOR]

This research reports on an analysis of personal network data collected from 70 HIV-positive HIV/AIDS patients (48 men, 22 women; 45 black, 25 white). Issues examined were the conditions surrounding the difficulty of knowing information about social network members, including knowledge of HIV status. The stigmatizing nature of AIDS resulted in selective knowledge regarding a person's HIV status (and other information) among their social network members. Informants' networks appeared smaller than those for other groups we have investigated, and this may be due to informant self-limiting, or alter rejection of HIV informant. These results will be useful in determining the amount of HIV + in the general population, and these methods could be applied to other hard-to-count populations. [ABSTRACT FROM AUTHOR]

Accurate estimates of the sizes of certain subpopulations are needed to inform important public policy decisions in the US. Laumann et al. (1989, 1993) have attempted to assess the accuracy of the reported data on the incidence of AIDS in the US, collected by the Centers for Disease Control and published in the AIDS Weekly Surveillance Reports (AWSR) and HIV/AIDS Surveillance Reports (HASR), by comparing these data with response data from the 1988, 1989, 1990 and 1991 General Social Surveys (GSSs). To establish reference comparison subpopulations, they did a similar assessment of the reported numbers of homicides during previous 12-month periods, published in the Unified Crime Report (UCR) and the Vital Statistics of the United States (VSUS), comparing these data with other response data from these same GSSs. The GSS data were compared with the AWSR, HASR, UCR and VSUS figures by sex, race, ethnicity, age, and region of the US. Their results for homicide victims are reasonably similar to the UCR and VSUS figures for these categories, while their results for AIDS victims are reasonably similar to the AWSR and HASR figures only for sex and age. There is then the question of whether reported total figures for the incidence of homicides and AIDS (as well as suicides during a previous 12-month period) are reasonably accurate. There is concern that there is significant undercounting of the total incidence of AIDS. Here we investigate this issue using a simple mathematical model of social networks, some elementary social theory, recent estimates of average personal network size in the US by the authors, and response data from the 1988, 1989, 1990, 1991 and 1993 GSSs. Assuming the average personal network sizes of homicide victims, suicide victims and AIDS victims are about the same as those for the general US adult population, we test as null hypotheses the propositions that the incidence of homicides reported in the UCR, of suicides reported in the VSUS, and of AIDS reported in the AWSR and HASR are accurate. Our analysis does not detect a significant inaccuracy in the reported figures for homicides. For suicides and AIDS, however, we encounter discrepancies of varying degrees, suggesting that either the reported figures are overcounts, AIDS and suicide victims have significantly smaller average personal network sizes than the general US adult population (smaller for AIDS victims than for suicides), or else the GSS respondents significantly underreported their personal knowledge of suicide and AIDS victims, either because they did not know that some of the people they know committed suicide or have AIDS, or because they falsely state their lack of knowledge of such victims, perhaps because of the stigma attached to such associations. These issues are illuminated by the results from an earlier survey of personal network size in Gainesville, Florida, and a previous national survey among surgeons, which suggest that lack of knowledge of personal network members who have AIDS seems to play a major role in explaining the discrepancies with the reported figures for AIDS. [ABSTRACT FROM AUTHOR]

Some methods for estimating the total size of personal communication networks are presented. All involve the scaling-up of a reported network size by a factor proportional to the number of people whom informants can recall when they are presented with a representative list of last names from a telephone directory. Estimates from Jacksonville, Florida give network sizes of 1700 ± 400; reevaluations of an estimate made for Orange County give 2025; and estimates from Mexico City give network sizes of about 600. The difficulties, and sources of error, in these estimates, are discussed. The estimates are compared with independent estimates based on the likelihood of informants knowing members of a small, countable subpopulation, which suggests for U.S. informants a network size of 1526. Thus consistent numbers are beginning to emerge, at least for U.S. informants. [ABSTRACT FROM AUTHOR]

This article compares four different methods for measuring personal social networks. One of these, often called an "emotional support group", is comprised of just a few intimates. People may call such intimates their "friends," but that word is also used to refer to a great many others who are not in the emotional support network. Another, usually larger, network is often called the "social support group." Many of the people in this network are also classified as "friends," but need not be. These are the people on whom one calls for a variety of favors. These two categories of networks are embedded in what we can call the "global network." This network, unlike the others, is well defined. It consists of all the people known to an individual, given a suitable definition of "knowing." It is assumed for this article that all the commonly used techniques for capturing lists of network members are valid. That is, they produce some subset of the global network which has an entity of its own.

This article reports a research designed to compare characteristics of the networks dredged by the General Social Survey (GSS) name generator and by the Reverse Small World technique (RSW). RSW is a standard list of 500 targets in a fictional small world problem. It was developed by P.D. Killworth and H.R. Bernard in 1978 order to: (1) get a an estimate of how many people are actually in anyone's average network and understand what differences in network size depends on; (2) investigate the nature of the penultimate links in a small-world study; (3) understand more about the decisions involved in the process of moving a folder across a set of small world links; (4) look for the rules governing who people know and why they know each other. Each target in RSW is supplied with information about occupation, location, hobbies, and other information needed by informants to make a first choice (first intermediary) on a small world chain to the target. The information supplied is generated by the informants themselves in a prior technique, called index.

The article presents a technique that allows mental maps of the world to be drawn from data on people's cognition about network relations. The technique produces both a holistic reproduction as well as specific elements that can be strictly (that is, numerically) compared. The study has produced two social network maps so far, one based on networks within the U.S., and the other based on informants' world networks. The U.S.-based network picture strongly resembles a geographic map of the U.S. Similarly, the world network map, to be discussed in this note, looks like a Mercator projection. Both maps are distorted. But the technique the article presents permits the systematic study of distortion in mental maps. That is, the difference between any mental map and any objective map (a Mercator projection, for example), or the difference between two or more mental maps (where both, presumably are distorted) may be observed. This opens the way to a systematic, cross-cultural study of how people store their complex social networks in their minds.

The article presents response by the authors to the critical comments made by sociologists R.S. Burt and William M. Bittner on the works of the authors. First, Burt and Bittner questioned the scope of the authors' article. They argue that one cannot extend the scope of the conclusions from one network analysis to other systems. In authors' view, this misses the point entirely. In the series of papers written on informant accuracy the authors have never drawn conclusions about the structure of any group studied, let alone extended any conclusions about social structure to other groups or to the world at large. What authors have been studying is not groups, but the methods by which most researchers have gathered data about groups. It is about these methods that authors have drawn a global generalization from their seven data sets: the method by which data are traditionally obtained (some variant of "who do you interact with") does not yield any reliable information whatsoever about who people in the group actually interact with.

This paper examines whether clique-structure in cognitive data (i.e. recall of who one talks to) may be used as a proxy for clique-structure in behavioral data (i.e. who one actually talks to). The answer to this question is crucial to much of sociometric and social net-theoretic studies of social structure. We analysed the clique structures of the communication patterns of four naturally occurring groups of sizes 34 to 58, whose actual communications could easily be monitored, together with the groups' perceptions of their communications. The groups used were: radio hams, a college fraternity, a group of office workers, and an academic department. The analysis used clique-finding, block-modelling, and factor-analytic techniques, all employed in such a way as to maximize the accuracy of the cognitive data. After defining a way to compare clique structures between behavioral and cognitive data, we found that there was no useful relationship between the two, and furthermore there was no significant difference in performance between any of the structure-finding algorithms. We conclude that cognitive data may not be used for drawing any conclusions about behavioral social structure. [ABSTRACT FROM AUTHOR]

This paper provides a comparison of the triadic-level structure inherent in behavioral and cognitive social network data taken on the same group, using a variety of groups whose communication could easily be monitored. It is found that many types of structure occur significantly more or less than chance in both behavioral and cognitive data, and providing that these are treated in similar ways, there is good agreement between the two structures. However, there are several ways to treat behavioral data, and these produce at least two essentially different structures. If cognitive and behavioral triads are compared, triad by triad, then there is virtually no agreement between them (even though they may both display the same structure on an overall triad census). Finally, as a demonstration of the dangers of relying solely on cognitive data, an unlikely null hypothesis is proposed. This asserts - for demonstration purposes - that, under many circumstances, behavioral structure never alters. Change in structure over time apparently occurs because of informant error in the reporting of the cognitive data. A pseudo-transition matrix, giving the probability that a triad is reported as one type when data are first taken, and a different type at a later date, is calculated. This compares reasonably with a genuine transition matrix evaluated for longitudinal cognitive data. It is believed that no data currently exist which can disprove this hypothesis, unlikely though it is. Much more accurate data are therefore necessary if any reliable theory of social structure is to be produced. [ABSTRACT FROM AUTHOR]

This paper is an attempt to examine and define the world network of a typical individual by discovering how many of his or her acquaintances could be used as first steps in a small-world procedure, and for what reasons. The town and occupation of each target was provided, together with the ethnic background, where this could not be inferred from the name. Starters were instructed in the small-world experiment and asked to write down their choice, amongst the people they knew, for the first link in a potential chain from them to each of 1267 targets. Starters provided information on each choice made (e.g. mother, cousin, friend, acquaintance, etc.) together with the sex of the choice) and the reason that choice had been made. The reason could be in one or more of four categories: something about the location of the target caused tile starter to think of his or her choice; the occupation of the target was responsible for the choice; the ethnicity of the target; or some other, unspecified, reason. Six main conclusions may be drawn from the data: (1) A mean of 210 choices per starter account for the "world" (i.e. the 1267 targets). This number is probably an underestimate. Only 35 choices are necessary to account for half the world, however, Of the 210, 95 (45%) were chosen most often for location reasons, 99 (4 7%) were chosen most often for occupation reasons, and only 7% of the chokes were mainly based on ethnicity or other reasons. (2) Chokes were mainly friends and acquaintances, with strong cleavage by sex. For any given target, the type of choke used by the majority of starters was a friend or acquaintance, and not family. For any given target, the most likely sex of the choice (i.e. over all starters) can be predicted accurately on 82% of occasions. This sex tends to be male, unless both starter and target are female, or if the target has a low-status occupation. Additionally, any given starter is most likely to pick a male choice for any target, except for the female starter-female target combination, when female choices are more likely. This was correct on 64% of occasions. (3) Location was the usual reason for choice (out of the four categories), with occupation second, and ethnicity or other reasons rarely used. This most popular reason for choice may be correctly predicted for any given target 81% of the time. (4) The decision as to which choke was made appears to depend primarily on the occupation of the target, and secondly on the distance (near/far) from Morgan town, West Virginia, where the experiment took place. (5) The expression "having one's man in ..." can be partially quantified. We may define a choke to "handle" a state in the U.S. if he or she was chosen for two-thirds or more of the targets in that state for which choices were made on the basis of location. Then, for any starter, on average, half the states are each handled by a single choice. (6) The accuracy of starters' recall about their networks is low, in the sense that their recall is incorrect more often than it is correct (i.e. their recall could not be put to any other use with any reliability). This confirms previous experiments on informant accuracy. [ABSTRACT FROM AUTHOR]