In , we show a portion of the social network, which demonstrates a clustering of moderately lonely (green nodes) and very lonely (blue nodes) people, especially at the periphery of the network. In the statistical models, the relationships between loneliness and number of social contacts proved to be negative and monotonic, as illustrated in and documented in .

To determine whether the clustering of lonely people shown in could be explained by chance, we implemented the following permutation test: we compared the observed network to 1,000 randomly generated networks in which we preserved the network topology and the overall prevalence of loneliness but in which we randomly shuffled the assignment of the loneliness value to each node (

Szabo & Barabasi, 2007). For this test, we dichotomized loneliness to be 0 if the respondent said they were lonely 0–1 days the previous week, and 1 otherwise. If clustering in the social network is occurring, then the probability that an LP is lonely given that an FP is lonely should be higher in the observed network than in the random networks. This procedure also allows us to generate confidence intervals and measure how far, in terms of social distance, the correlation in loneliness between FP and LP reaches. As described below and illustrated in , we found a significant relationship between FP and LP loneliness, and this relationship extends up to three degrees of separation. In other words, a person’s loneliness depends not just on his friend’s loneliness, but also extends to his friend’s friend and his friend’s friend’s friend. The full network shows that participants are 52% (95% C.I. 40% to 65%) more likely to be lonely if a person they are directly connected to (at one degree of separation) is lonely. The size of the effect for people at two degrees of separation (e.g., the friend of a friend) is 25% (95% C.I. 14% to 36%) and for people at three degrees of separation (e.g., the friend of a friend of a friend) is 15% (95% C.I. 6% to 26%). At four degrees of separation, the effect disappears (2%, 95% C.I. –5% to 10%), in keeping with the “three degrees of influence” rule of social network contagion that has been exhibited for obesity, smoking, and happiness (e.g., (

Christakis & Fowler, 2007;

Christakis & Fowler, 2008;

Fowler & Christakis, 2008).

The first model in , depicted in the first three columns, shows that: (1) loneliness in the prior wave predicts loneliness in the current wave; and (2) current feelings of loneliness are much more closely tied to our networks of optional social connections, measured at the prior wave, than to those that are handed to us upon birth or to demographic features of the individuals. People with more friends are less likely to experience loneliness in the future, and each extra friend appears to reduce the frequency of feeling lonely by 0.04 days per week. That may not seem like much, but there are 52 weeks in a year, so this is equivalent to about two extra days of loneliness per year; since, on average (in our data) people feel lonely 48 days per year, having a couple of extra friends decreases loneliness by about 10% for the average person. The same model shows that the number of family members has no effect at all.

Analyses also showed that loneliness shapes social networks. Model 2 in , depicted in the middle three columns, shows that people who feel lonely at an assessment are less likely to have friends by the next assessment. In fact, compared to people who are never lonely, they will lose about 8% of their friends on average by the time they take their next exam in roughly four years. For comparison, and not surprisingly, the results depicted in the third model in (last three columns) show that loneliness has no effect on the future number of family members a person has. These results are symmetric to both incoming and outgoing ties (not shown – available on request) – lonely people tend to receive fewer friendship nominations, but they also tend to name fewer people as friends. What this means is that loneliness is both a cause and a consequence of becoming disconnected. These results suggest that our emotions and networks reinforce each other and create a rich-gets-richer cycle that benefits those with the most friends. People with few friends are more likely to become lonelier over time, which then makes it less likely that they will attract or try to form new social ties.

We also find that social connections and the loneliness of the people to whom these connections are directed interact to affect how people feel. shows the smoothed bivariate relationship between the fraction of a person’s friends and family who are lonely at one exam, and the number of days per week that person feels lonely at the following exam. The relationship is significant and adds an extra quarter day of loneliness per week to the average person who is surrounded by other lonely people compared to those who are not connected to anyone who is lonely. In , we present a statistical model of the effect of lonely and non-lonely LPs on future FP loneliness that includes controls for age, education, and gender. This model shows that each additional lonely LP significantly increases the number of days a FP feels lonely at the next exam (p<0.001). Conversely, each additional non-lonely LP significantly *reduces* the number of days a participant feels lonely at the next exam (p=0.002). But these effects are asymmetric: lonely LPs are about two and a half times more influential than non-lonely LPs, and the difference in these effect sizes is itself significant (p=0.01). Thus, the feeling of loneliness seems to spread more easily than a feeling of belonging.

To study person-to-person effects, we examined the direct ties and individual-level determinants of FP loneliness. In the GEE models we present in – we control for several factors as noted earlier, and the effect of social influence from one person on another is captured by the “Days/Week LP Currently Lonely” coefficient in the first row. We have highlighted in bold the social influence coefficients that are significant. summarizes the results from these models for friends, spouses, siblings, and neighbors. Each extra day of loneliness in a “nearby” friend (who lives within a mile) increases the number of days FP is lonely by 0.29 days (95% C.I. 0.07 to 0.50, see first model in ). In contrast, more distant friends (who live more than a mile away) have no significant effect on FP, and the effect size appears to decline with distance (second model in ). Among friends, we can distinguish additional possibilities. Since each person was asked to name a friend, and not all of these nominations were reciprocated, we have FP-perceived friends (denoted “friends”), “LP-perceived friends” (LP named FP as a friend, but not vice versa) and “mutual friends” (FP and LP nominated each other). Nearby mutual friends have a stronger effect than nearby FP-perceived friends; each day they are lonely adds 0.41 days of loneliness for the FP (95% CI: 0.14 to 0.67, see third model in the third column of ). In contrast, the influence of nearby LP-perceived friends is not significant (*p*=0.25, fourth model in the fourth column of ). If the associations in the social network were merely due to confounding, the significance and effect sizes for different types of friendships should be similar. That is, if some third factor were explaining both FP and LP loneliness, it should not respect the directionality or strength of the tie.

We also find significant effects for other kinds of LPs. Each day a coresident spouse is lonely yields 0.10 extra days of loneliness for the FP (95% CI: 0.02 to 0.17, fifth model in ), while non-coresident spouses have no significant effect (sixth model). Next-door neighbors who experience an extra day of loneliness increase FP’s loneliness by 0.21 days (CI 0.04 to 0.38, third model in the third column of ), but this effect quickly drops close to 0 among neighbors who live on the same block (within 25M, fourth model in ). All these relationships indicate the importance of physical proximity, and the strong influence of neighbors suggests that the spread of loneliness may possibly depend more on frequent social contact in older adults. But siblings do not appear to affect one another at all (even the ones who live nearby, see first model in ), which provides additional evidence that loneliness in older adults is about the relationships people choose rather than the relationships they inherit. And spouses appear to be an intermediate category; shows that spouses are significantly less influential than friends in the spread of loneliness from person to person (as indicated by the significant interaction term in the first row).

| **Table 6**Influence of Type of Relationship on Association Between LP Loneliness and FP Loneliness |

Analyses separated by gender suggested that loneliness spreads more easily among women than among men, and that this holds for both friends and neighbors. As shown in the coefficients in the first row of and , women are both more likely to be affected by the loneliness of their friends () and neighbors (), and their loneliness is also more likely to spread to other people in their social network. The coefficients in bold show that social influence is greatest when the FP or the LP is female. Women also reported higher levels of loneliness than men. We are reporting estimates from a linear model, however, so the baseline rate of loneliness should not affect the absolute differences that we observed. (We would be more concerned about this possible effect if we were reporting odds ratios or risk ratios that are sensitive to the baseline.) In a linear model, any additive differences in baseline should be captured by the sex variable in the model, which does show a significantly higher baseline for women. However, since we include this control, the baseline difference in men and women should not affect the interpretation of the absolute number of days each additional day of loneliness experienced by an LP contributes to the loneliness experienced by an FP.

| **Table 7**Association of LP Loneliness and FP Loneliness in Friends, By Gender |

Finally, our measure of loneliness was derived from the “I feel lonely” item in the CES-D. To address whether our results would change if depression were included in the models, we created a depression index by summing the other 19 questions in the CES-D (dropping the question on loneliness). The Pearson correlation between the indices in our data is 0.566. If depression is causing the correlation in loneliness between social contacts, then the coefficient on LP loneliness should be reduced to insignificance when we add depression variables to the models in . Specifically, we add a contemporaneous and lagged variable for both FP’s and LP’s depression. The results in and show that there is a significant association between FP current depression and FP current loneliness (the eighth row in bold), but other depression variables have no effect and adding them to the model has little effect on the association between FP and LP loneliness. Loneliness in nearby friends, nearby mutual friends, immediate neighbors, and nearby neighbors all remain significantly associated with FP loneliness.