Why Your Friends Are More Important and Special ThanYou ThinkThomas U. GrundStockholm University

Abstract: A large amount of research finds associations between individuals’ attributes and the position of individuals innetwork structures. In this article, I illustrate how such associations systematically affect the assessment of attributesthrough network neighbors. The friendship paradox—a general regularity in network contexts, which states that yourfriends are likely to have more friends than you—becomes relevant and extends to individuals’ attributes as well. First,I show that your friends are likely to be better informed (closeness), better intermediaries (betweenness) and morepowerful (eigenvector) than you. Second, I suggest more generally that your friends are likely to be more special in theirattributes than the population at large. Finally, I investigate the implications of this phenomenon in a dynamic setting.Applying calibrated agent-based simulations, I use a model of attribute adoption to emphasize how structurally introducedexperiences penetrate the trajectory of social processes. Existing research does not yet adequately acknowledge thisphenomenon.

Keywords: social networks; centrality; network neighbors; friendship paradox; agent-based simulations; analyticalsociologyEditor(s): Jesper Sørensen, Ezra Zuckerman; Received: December 14, 2013; Accepted: December 27, 2013; Published: April 14, 2014

Citation: Thomas U. Grund. 2014. “Why Your Friends Are More Important and Special Than You Think.” Sociological Science 1: 128–140. DOI:10.15195/v1.a10

Copyright: c© 2014 Grund. This open-access article has been published and distributed under a Creative Commons Attribution License, which allowsunrestricted use, distribution and reproduction, in any form, as long as the original author and source have been credited.

Alarge number of studies find associations be-tween the positions of individuals in social

networks (i.e., centrality) and their attributes,such as tendency to innovate (Tsai 2001), jobsearch success (Granovetter 1973), performance(Brass et al. 2004), or even good looks (Mul-ford et al. 1998; Tong et al. 2008). In general,such associations are either the result of centralindividuals adopting certain attributes (such asopinions), or alternatively, of network ties evolv-ing around individuals with certain attributes.An important and overlooked aspect, however, isthe way in which such associations affect the expe-rienced distribution of attributes among networkneighbors.

Social scientists have long been aware thatsocial structure by itself limits what individualsobserve and that it also affects individuals’ viewsof the world. Several decades ago, Feld and Grof-man (1977) introduced the class size paradox—also known in the literature as the friendshipparadox. In its simplest form, this paradox pos-tulates that the perceived size of groups is largerthan it actually is. Feld and Grofman used the

example of college classes with varying sizes, inwhich most of the students in the classes expe-rience a mean class size that is greater than thetrue mean. This is due simply to the fact thatmore students find themselves in larger classes;hence, more students have the experience of beingin a large class than being in a small class. Conse-quently, if one were to ask students about the sizeof their classes and calculate the mean, one wouldderive a systematically inflated estimate. Feld(1991) applied this strikingly simple idea to socialnetwork contexts and showed that your friends—on average—have more friends than you do. Therationale for this regularity is straightforward: in-dividuals with many friends simply appear moreoften in dyadic relationships, resulting in a sys-tematic mismatch in the distribution of numberof friends and the distribution of friends’ numberof friends.

The general argument of this article is thatwhen there is an association between an attributeand the network position of individuals—no mat-ter how it came about in the first instance—simple embeddedness in network structure gen-

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erates a condition where not only the number offriends’ friends, but also the attributes of friendsare no longer random (see also Eom and Jo 2014).Following the logic of the friendship paradox,the fact that individuals with many friends ap-pear more often in dyadic friendship relationshipsmeans that when an attribute is correlated withnetwork position, some values of the attributeare systematically overrepresented in the assess-ment of friends’ attributes. As soon as thereis a correlation between network position andsome actor attribute and not everybody has thesame number of friends (both conditions are eas-ily met in most empirical settings), exposure tothe attributes of others through networks is sys-tematically affected. The existing literature doesnot adequately acknowledge this phenomenon.

This article elaborates on this in three differ-ent ways. First is a discussion of the relevanceof the phenomenon for the assessment of othernetwork features. I show that your friends arelikely to be better informed (closeness), betterintermediaries (betweenness), and more powerful(eigenvector) than you. Second, I outline howthe same logic applies to individuals’ attributesas well. It is likely that your friends are morespecial in their attributes than the populationat large. Third, I investigate the implications ofthe friendship paradox in a dynamic setting. Ap-plying calibrated agent-based simulations, I usea model of attribute adoption to emphasize howstructurally introduced experiences penetrate thetrajectory of social processes. The study empha-sizes a previously ignored aspect of the assess-ment of individuals’ attributes through networkneighbors.

CentralityOne arena where this phenomenon plays out isthe importance or centrality of nodes in networks.Social network scholars have spent considerableeffort developing indicators of centrality as a wayto describe individuals’ positions in social net-works. Centrality is important because it indi-cates who occupies critical positions in the net-work. Furthermore, a large array of attributes,such as popularity, opinion leadership, innovation,performance in work teams, individuals’ stand-ing in criminal networks, and many more have

been associated with it (Ibarra 1993; Morselli,Giguère, and Petit 2007). Various argumentshave been brought forward as to what differ-ent centrality measures actually mean, wherethey make sense, and what concepts they repre-sent (Borgatti and Everett 2006; Freeman 1978;Friedkin 1991; Marsden 2002). Perhaps the mostfrequently used centrality measures are degree,closeness, betweenness, and eigenvector. Thefirst three were proposed by Freeman (1978), andeigenvector was proposed by Bonacich (Bonacich1972; 1987).

Degree centrality is the most straightforwardand intuitive measure. It simply counts, for eachindividual, the number of outgoing (out-degree)and incoming (in-degree) relationships or networkties. When a network is undirected (network tiesdo not distinguish between origin and destina-tion), in- and out-degree are the same and arecalled simply degree. Because of its relative sim-plicity, degree centrality comes easily to mind,and it has been the sole focus of study of thefriendship paradox so far (Christakis and Fowler2010; Feld 1991). However, degree centralityis a rather local concept. It does not considerthe network structure at large but focuses onthe immediate network environment (number offriends). Let yij be a network, where yij = 1means there is a network tie between node i andnode j and yij = 0 means there is none. Foran undirected network, degree centrality of nodenode i is defined as Cdegree (i) =

∑j

yij .

In contrast, closeness centrality considers thedistance from one actor to all other actors—nomatter how far away they are. An actor’s close-ness centrality is defined as the inverse of thesum of the number of steps it takes to reach allother actors (in the shortest way) (Freeman 1978).Other definitions focus on random walks: on av-erage, how many random steps from one actorto another would it take to reach a focal node(Noh and Rieger 2004)? In any case, closeness isa measure of the speed with which informationcan spread to the focal actor and is often asso-ciated with how well individuals are informedabout what happens elsewhere. Higher scoresmean that, on average, it takes fewer steps toreach others in the network from this actor; lowerscores require longer paths. Usually, the calcu-lation of closeness scores requires the network

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to be connected and undirected. Formally, it isdefined as Ccloseness (i) =

∑j

[dij ]−1, where dij is

the length of the shortest path from node i tonode j.

Betweenness centrality measures the extentto which a focal actor lies between other actors(Freeman 1978). It is defined as the number ofshortest paths (or geodesics) from all actors toall others that pass through the focal node. Adefinition based on random walks has been pro-posed here as well: conducting a random walkthrough the network, how many times wouldone pass the focal actor (Newman 2005)? Bothcloseness and betweenness are far more nuancedthan degree. An actor may have few friends butstill play an important role in the transmissionof information through the network as a whole.Betweenness therefore captures the importanceof actors as intermediaries or brokers. An actorwith high betweenness centrality can potentiallyinfluence the spread of information through thenetwork by facilitating, hindering, or even alter-ing the communication between others (Freeman,1978; Newman, 2003). It is computed as follows:Cbetweenness (i) =

∑s

∑t

σst(i)σst

, where s and t are

nodes in the network different from i, σst de-notes the number of shortest paths from s to t,andσst (i) is the number of shortest paths from sto t that go through i.

Finally, eigenvector centrality is based on theidea that those individuals whose network neigh-bors are central ought to be more central thanthose whose neighbors are not (Bonacich 1972;Bonacich 1987). Mathematically, scores corre-spond to the values of the first eigenvector of theadjacency matrix that defines the network. Inmore detail, the centrality of each actor is pro-portional to the sum of the centralities of thoseactors to whom he or she is connected. Onecan think of eigenvector as a recursive versionof degree centrality. Not just the individual’sdegree matters, but the degree of those withwhom one is connected with as well (and so on).In diffusion contexts, eigenvector centrality iscrucial; it captures the idea of multiplied riskand power. Eigenvector centrality is defined as:Ceigenvector (i) = vi =

1λmax(Y ) ·

∑j

aji · vj , with

v = (v1, . . . , vn)T referring to an eigenvector for

the maximum eigenvalue λmax (Y ) of the adja-cency matrix Y , representing the network.

Each of these measures accounts for the promi-nence of individuals in social networks, but thereare considerable conceptual differences betweenthem. Although the different measures of central-ity are often correlated, they do not necessarilyhave to be (Bolland 1988; Rothenberg et al. 1995;Valente et al. 2008), and the mathematical rela-tionships between them are far from obvious.

So far, the friendship paradox has been exclu-sively thought of in terms of degree centrality. Atthe time the paradox was discovered, researchershad just begun to investigate nuances betweencentrality measures and how they are associatedwith different aspects of social life. But whatabout the closeness, betweenness and eigenvectorscores of friends? Does the friendship-paradoxhold here as well? Are your friends, on average,more important than you?

Figure 1 shows a network of mutual friend-ships among eight girls at “Marketville” highschool. While names are fictitious, the data stemfrom Coleman’s (1961) The Adolescent Society ;Feld (1991) also uses this example. In Table 1,the first column indicates the number of friends(degree) an individual has and the second columnthe average number of friends’ friends (mean de-gree of friends), as provided in Feld (1991:1466).The next columns give scores for closeness, be-tweenness, and eigenvector centrality. On aver-age, individuals’ friends seem not only to havemore friends themselves (degree), but are alsobetter informed (closeness), are more likely to bebrokers (betweenness), and are also more power-ful (eigenvector). (See Table 1, last row).

In order to confirm these findings on a largerscale, I draw on the the Dynamics in Networks(DyNet) study’s friendship networks in 14 U.S.schools. Data were collected in middle schoolsin Oregon and California between fall 2008 andspring 2012. All members of the participatingmiddle schools (usually grades six to eight) wereinterviewed four times each academic year. Stu-dents were asked to fill out a questionnaire ondemographic characteristics. Furthermore, theywere asked to choose from a list of all participat-ing pupils in their school the ones they spendtheir free time with. As an example, Figure 2shows the largest component of the network of“Cascade” middle school, with 243 individuals and

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Figure 1: Friendships among eight girls in “Marketville” high school

Figure 1: Friendships among eight girls in “Marketville” high school

517 undirected friendship ties. All actors whosedegree is smaller than the average degree of theirfriends are colored in white; those whose degreeis larger than the average degree of their friendsare colored in grey.

Based on the complete DyNet data, Figure 3shows results of centrality and friends’ centralitycalculations. Each school is represented by onedata point. The x axis shows the average cen-trality score for all students in the school. The yaxis shows the average centrality of friends. Bothscores are derived the same way as the valueslisted at the bottom row of Table 1. The resultsclearly indicate that, on average, friends havemore friends (degree), are better informed (close-ness), are more likely to be brokers (betweenness),and are also more powerful (eigenvector) thanthe average student. All data points are in theupper left triangles of the graphs. Hence, thesefindings suggest that the friendship paradox isnot limited to having more friends but extendsto a wide range of other network features as well.

Individual attributesMore generally, the same logic applies to anyindividual attribute correlated with degree cen-trality. In order to illustrate the validity andimplications of this intuition, I create simulationsusing two networks: the real friendship networkof “Cascade” middle school as shown in Figure2 and an Erdõs–Rényi network with exactly the

same number of nodes (243) and undirected ties(517). The first network represents a real network,where all sorts of factors played a role in the emer-gence of ties. The second network is based onrealistic assumptions about the number of friend-ship ties, but structural configurations such astriads are ignored; all ties have the same prob-ability of existing independently of each other(random graph). In both networks I assign allactors an artificial attribute x, which is drawnfrom a normal distribution with a mean of zeroand a standard deviation of one. The values ofx can be allocated to individuals in such a waythat x is correlated with the number of friends(Degree) the individuals have. This is achievedwith the corgen command, a built-in function ofthe R package ecodist. Other major statisticalsoftware packages have similar functions. In thecurrent case, I artificially change the correlationbetween x and Degree from 0 to 0.9 in steps of0.1; for each configuration I repeat this 100 times.For each combination of network, correlation,and repetition, one can calculate how individualsexperience their friends in terms of x. Each indi-vidual is assigned a score that is the mean of theindividual’s friends’ attribute x. These scores aresimilar to the mean degree of friends’ entries inTable 1. I then calculate, for each combination ofnetwork, correlation, and repetition, the averagescore of x for all individuals (grand mean valueof x) and the average score with regards to howall individuals perceive their friends on x (friendsmean value of x). These scores correspond to

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Table 1: Summary of individual’s network characteristics and mean network characteristics of friends

Degree

MeanDegreeof

Friend

s

Closeness

MeanCloseness

ofFriend

s

Betweenn

ess

MeanBetweenn

essof

Friend

s

Eigenvector

centrality(E

C)

MeanEC

offriend

s

Betty 1.00 4.00 0.06 0.09 0.00 7.50 0.30 0.93Sue 4.00 2.75 0.09 0.08 7.50 4.13 0.93 0.71Alice 4.00 3.00 0.09 0.08 5.50 4.63 1.00 0.77Jane 2.00 3.50 0.06 0.08 0.00 3.25 0.60 0.91Pam 3.00 3.33 0.09 0.08 10.00 6.33 0.71 0.73Dale 3.00 3.33 0.07 0.08 1.00 4.33 0.82 0.84Carol 2.00 2.00 0.07 0.07 6.00 5.00 0.26 0.40Tina 1.00 2.00 0.05 0.07 0.00 6.00 0.09 0.26

Average 2.50 2.99 0.07 0.08 3.75 5.15 0.59 0.69

the entries in the bottom row of Table 1. Fi-nally, I calculate the difference between these twovalues and divide it by the standard deviationof this difference over all individuals. In Figure4, I use boxplots to illustrate the results of thesimulation analyses. The x axis shows the artifi-cially assigned correlation between x and Degreeand the y axis shows the standardized deviationbetween true and perceived average scores of x.The data points in the boxplot correspond to the100 repetitions I used for each combination.

The results are striking. Weak correlations—as low as 0.1—between x and Degree suffice togenerate a significant difference between the trueand experienced average scores of x. Obviously,as the correlation increases, this difference be-comes even more pronounced. Interestingly, de-spite having the same number of actors and net-work ties, there is also quite a difference betweenthe real “Cascade” middle school network andthe Erdõs–Rényi network with the same density.The effect appears twice as large in the real worldnetwork as in the random network. Hence theactual network configuration seems to matter aswell. In the empirically calibrated setting, the

effect is more pronounced than in the stylizedsimulation.

So far, I have only focused on static aspects ofthe friendship paradox. Your friends are likely tohave more friends than you do. I have argued thatthe phenomenon should be viewed more generallyand extends to all sorts of individual attributesthat are correlated with the number of friendsindividuals have.

What does that imply? Does the friendshipparadox only affect what individuals experienceat a specific moment in time or does it also system-atically affect the trajectory of social processes,where the behavior or attributes of individualsinfluence the behavior or attributes of other indi-viduals?

Attribute adoptionA complex systems point of view, as for exampleadvocated by Thomas Schelling (1971), empha-sizes the way in which social phenomena emergeor disappear in light of the interdependenciesamong the individuals or elements constituting

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Grund Why Your Friends Are More ImportantFigure 2: Friendship network of “Cascade” middle school

Figure 2: Friendship network of “Cascade” middle school

a socioeconomic system. A social outcome, suchas the prevalence of an attribute in a popula-tion, is not simply the aggregation of individuals’attributes. Instead, each individual’s behaviorchanges the conditions for other individuals’ ac-tions, adoption of certain attributes, and so on.

In order to investigate the role of the friend-ship paradox in such a context, I draw on asimple agent-based model of attribute adoption.Agent-based models simulate the emergence ofbroader macro-level phenomena from the bottomup. Agents, representing virtual counterpartsof individual actors, are situated within social,structural, and normative environments (Gilbert2008). The behavior of agents, in combinationwith interactions between agents, is shown to pro-duce broader macro-level trends. This methodis particularly appropriate for studying socialdynamics.

Assuming that individuals adopt the attributes(or behaviors) of others, the question is whetherthe systematic exposure to others’ attributes im-plied by the friendship paradox leads to a differentdistribution of the attributes in the populationat large compared to a scenario where that dis-tortion is absent.

As before, our simulation starts with thefriendship network of “Cascade” middle school.By calibrating the structure of the simulation

with an empirically observed network, I createrealistic conditions for the aspect of the simula-tion where the friendship paradox applies, thedegree distribution. I focus on the attribute x ofindividuals and assume that x can be changed—xcan stand for opinion, clothing style, or anythingelse—and that the values of x are drawn from anormal distribution with mean score zero and astandard deviation of one. As before, the valuesof x are allocated to individuals in the social net-work in such a way that x is correlated with thenumber of friends (Degree) the individuals have.Once again, this is achieved with the built-incorgen command of the R-package ecodist. Thistime I artificially change the correlation betweenx and Degree from 0 to 0.8 in steps of 0.2.

Next, I apply a simple algorithm of attributeadoption in which at each point in time one ran-domly selected individual adopts the attribute ofanother individual. This can occur in two differ-ent ways: 1) A randomly selected actor copies theattribute of another randomly selected actor; or2) A randomly selected actor copies the attributeof a randomly selected friend. In both cases, theindividual who adopts the attribute and the in-dividual whose attribute is adopted are selectedat random, with the only difference being thatin the latter scenario individuals can only copyfrom friends. In this way, the second scenario

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Figure 3: Average centrality and average centrality of friends in 14 schools in the United States

Figure 3: Average centrality and average centrality of friends in 14 schools in the United States

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Figure 4: Experienced and true value of attribute x (correlated with Degree)

Figure 4: Experienced and true value of attribute x (correlated with Degree)

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incorporates the friendship paradox, whereas thefirst scenario represents a baseline case where thefriendship paradox is blended out. Comparingsimulation results from both scenarios allows oneto draw conclusions about the dynamic impli-cations of the friendship paradox for attributeadoption.

Figure 5 shows results of a typical simulationrun. One the left side I present the starting dis-tribution of the attribute x. The shading on theright side of Figure 5 illustrates the results ofa simulation run with no correlation between xand Degree and the whole population as poten-tial reference point (at each time one randomlyselected actor copies the attribute of another ran-domly selected actor). For simplicity, there isno error in attribute adoption and no mutation.Neither would change the results, but their in-clusion would distract from the point we want tomake. The shading on in the right side of Figure5 stands for the density distribution of attributex. This is a simplified way to present the distri-bution of x, as on the left (start), but at differenttimes during the simulation. All simulations arerun in NetLogo 5.0.3 (Wilensky 1999) using theR extension (Thiele, Kurth, and Grimm 2012) tofacilitate seamless communication between theagent-based modeling and the statistics software.

Because actors only copy the attribute andmake no alterations, the convergence in x thatis found makes sense. At some point in time,every actor has the same value on x. Although,in principle, all initial values of x could be apoint of convergence, the original distribution ofxmatters a lot.

In Figure 6, I present repeated simulation re-sults in which two parameters of the simulationare changed. First, as in the preceding analysis, Ialter the correlation between x and Degree. Thisis represented by a sub-graph for each correlation.Next, as described above, I restrict the referencegroup from which the randomly selected actorcan copy the attribute to friends only. In theRandom scenario (white bars), the selected actorcopies the attribute from a randomly selectedother actor. In the Friends scenario (grey bars),the selected actor copies the attribute from arandomly selected friend. For all combinationsof correlation and scenario, the simulation is re-peated 100 times with different starting valuesof x. A simulation run ends when convergence is

reached and all actors have the same value on x.The boxplots in Figure 5 show the convergencevalues for the repeated simulations.

As one might expect, in the baseline Randomscenario, the convergence values follow the samedistribution of the initial values of x. Correla-tion between attribute score and network degreehas no effect. When individuals copy the at-tribute value from a friend, the results are differ-ent. With increasing correlation Corr(x,Degree)at the start of the simulation, the convergencevalues of the simulation increase as well. Scoresare typically above zero. This is interesting par-ticularly because the original distribution of theattribute is exactly the same in both scenarios.This example shows that distortions introducedby the friendship paradox are not limited to thestatic perception of attributes or network posi-tions. In fact, the distorted individual experienceof the world that the paradox implies can actu-ally change the world compared to the world thatwould have resulted from accurately perceptions.

Discussion and conclusionA tradition in sociological thinking suggests thatsocial phenomena (macro-level) both influencewhat individuals (micro-level) do and are theresult of many individuals behaving in certainways (Coleman 1990). Interdependencies betweenindividuals are considered to be crucial to thisprocess; the behavior of one individual changesthe conditions for the actions of other individu-als. In consequence, social phenomena are notsimply the aggregate of separate individuals’ de-cisions but the complex outcome of the dynamicinterplay of individuals’ behaviors. Agent-basedmodels are a useful tool for analyzing such dy-namics (Gilbert 2008).

This article focuses on an often neglected as-pect of this phenomenon. Individuals base theirdecisions on what they think the social worldlooks like, but their assessments of others’ at-tributes are systematically off from the true val-ues in the population.

The friendship paradox is a purely structuralperspective, postulating that in social networkcontexts, individuals—on average—experiencetheir friends as having more friends than them-selves. The deductive logic underlying this phe-

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Grund Why Your Friends Are More ImportantFigure 5: Starting distribution and convergence of a typical run

Figure 5: Starting distribution and convergence of a typical run

Figure 6: Convergence points with different correlations between attribute and degree

Figure 6: Convergence points with different correlations between attribute and degree

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nomenon is that heterogeneity in individuals’numbers of friends translates into more popularindividuals being present in more dyadic friend-ship relationships, with the result being a system-atic mismatch in the distributions of number offriends and number of friends’ friends.

So far, the friendship paradox had been ex-clusively thought of in terms of degree centrality.This article argues for a more general perspectiveand an extension of the concept to a wide range ofnetwork features and individual attributes. Sim-ple embeddedness in a (heterogeneous) networkstructure generates conditions where individu-als who are more important in terms of close-ness, betweenness, and eigenvector centrality aremore prevalent in friendship relationships as well.Hence the friends of a randomly selected sam-ple of individuals are likely to occupy structuralpositions that are not representative of the popu-lation at large. On average, your friends not onlyhave more friends (degree), but are also betterinformed (closeness), better intermediaries (be-tweenness), and more powerful (eigenvector) thanyou. Furthermore, the findings show that individ-uals’ attributes are affected by the phenomenon.Even weak correlations between network positionand actor attributes, which are present in manyempirical settings, suffice to generate a situationwhere the friends of a randomly selected sample ofindividuals have significantly different attributesthan the individuals in the original sample. Purelogic dictates that, for example, your friends areon average better looking than you.

Finally, I introduced an agent-based model ofattribute adoption to illustrate the implications ofthe friendship paradox in a dynamic setting. Theresults clearly reveal that distortions of individ-uals’ experience of the social world, introducedby nonrepresentative friends, persist and leadto different social outcomes compared to whenindividuals are not limited by their friendshiprelationships. Though an attribute may beginequally distributed among a virtual population,a simple process of attribute adoption leads toconvergence at different values when the referencegroups is changed. Hence, a situation where thefriends of a randomly selected sample of individ-uals have significantly different attributes thanindividuals in the original sample, as implied bythe friendship paradox, can change the trajectory

of social processes in which individuals influenceeach other.

These findings have several important impli-cations that have so far been mostly overlookedin the literature. For instance, individuals can beperfectly accurate in assessing themselves in rela-tion to their friends but still be systematically offwhen it comes to the population at large, simplybecause their friends are not representative.

Several testable hypotheses follow from this.For example, nonrepresentative exposure to oth-ers’ attributes will be most pronounced whenboth heterogeneity in degree distribution and cor-relation between attribute and degree are high.This can affect individuals’ assessment of the realworld. In contexts where individuals do not relyon friends for making assessments about the dis-tribution of an attribute in a population, it maynot matter that much. If, however, individualsheavily rely on friends to make inferences abouta population as a whole, they will systematicallyoverestimate the mean of such an attribute. Inturn, the evaluation of one’s own position or at-tribute in relation to the population as a wholewill be misaligned. Hence, false assessments inrelation to others should be more likely for at-tributes where individuals are less likely to obtainobjective reference points from the populationbut have to draw on their experiences with theirown friends instead.

In addition, the friendship paradox can be cru-cial for identifying hidden subpopulations. Forexample, in criminal contexts one often wants tofind important criminals. A straightforward ap-plication of these insights would be to track downthe co-offenders of a randomly selected group ofoffenders. By definition, the group of co-offenderswill be more important in the criminal networkas a whole and exhibit non-random attributes.The implications of the friendship paradox asdiscussed in this article offer tremendous poten-tial for the identification of such actors in hiddenpopulations. As I illustrate, the friends of a ran-domly selected group exhibit certain non-randomattributes, which makes them nonrepresentativefor the population at large. Sometimes, how-ever, getting access to such nonrepresentative,important individuals is exactly what one wants.

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Thomas U. Grund: Institute for Futures Studies,Stockholm, Sweden; Department of Sociology,Stockholm University, Sweden.E-mail: thomas.u.grund@gmail.com.

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