## Introduction

The strength of social relations has been shown to affect an individual’s access to innovation1, access to economic opportunities2, life expectancy3, and happiness4. According to Granovetter’s classic theory about tie strength5, information flows through social ties of two strengths. First, through weak ties. These ties, despite being used infrequently, bridge distant groups that tend to posses diverse information, facilitating the knowledge dissemination across communities. Second, information also flows through strong ties. These ties, by being used frequently, knit close communities together, and represent dependable sources of social and emotional support.

To date, however, the correspondence between tie strength and population’s economic prospects has not been quantified, largely because of the inability to operationalize tie strength based on Granovetter’s conception. Typically, network studies operationalize strength with indicators like frequency or volume of contact6. Eagle et al. did so by studying the relationship between the structure of a national communication network and access to socio-economic opportunity7. They found that network diversity was associated to opportunities, but communication volume or number of contacts was not. The prospect that tie strength is not a unidimensional construct ranging from weak to strong but might be multidimensional is broadly consistent with theoretical and experimental work by Marsden and Campbell6 and Wellmann and Wortley8. It is also consistent with Granovetter’s original operationalization of strength as “a (probably linear) combination of the amount of time, the emotional intensity, the intimacy (mutual confiding), and the reciprocal services which characterize the tie.”5 These indicators have been repeatedly found to be only weakly related to frequency of contacts6,7. Therefore, network studies using frequency of contacts to model strength are capturing only one aspect of the linkages among individuals.

Our work departed from the premise that tie strength is a unidimensional construct, built upon work on social psychology starting from Granovetter’s conception of tie strength, and identified and validated ten fundamental dimensions of social relationships9,10. In previous work, we showed that these ten dimensions correspond to how people perceive and categorize most of their own social relationships9, and we built a state-of-the-art NLP tools to infer the presence of these dimensions from textual communication10. In this work, we used these tools to analyze a large conversation network of geo-referenced Reddit users across the entire US ($$\sim$$13M ties). Then, going back to Eagle et al.’s work and borrowing their methodological framework7, we were able to test whether the structure of a national communication network (in particular, its tie diversity) was related to access to socio-economic opportunities, and whether switching from a unidimensional notion of tie strength to a multidimensional one would improve explanatory power. We found that tie diversity measured on the networks of knowledge exchange and social support correlates much more strongly with economic development ($$R^2=0.62$$) than diversity measured on a network simply weighted on frequency of interactions ($$R^2=0.30$$).

In line with Granovetter’s conception of tie strength, we found that knowledge ties and social support ties: are hardly distinguishable solely based on frequency of interaction; have opposite geographic distribution (knowledge ties are global, spanning longer geographical distances, while social support ones are local, typically staying in the same state); and both contribute to economic opportunities (states with higher GDP per capita are characterized by both global access to knowledge and local access to support). These results point to the importance of developing multidimensional measures of tie strength in network theory to better reflect the nature of human relationships that social links ought to model.

## Results

From a set of 65M comments posted on Reddit by 1.3M users between the years of 2006 and 2017, we extracted the social interactions of all Reddit users that we could geo-reference at the level of the 51 US states using high-accuracy heuristics validated in previous work (see “Methods”). In Reddit, conversations develop over discussion threads. If user i commented over either a submission or a comment of another user j, we considered that i sent a message to j, as it is common practice when studying Reddit conversation networks11. We created a directed communication graph $${\mathscr {G}}(U,E)$$ to model such exchange of messages. The set of nodes U contains all the geo-referenced Reddit users in our dataset. Two users i and j are connected by a directed edge $$(i, j, w(i, j)) \in E$$ if user i sent at least one message to user j. The edge weight w(ij) represents the frequency of contacts and it is equal to the total number of messages sent. In total, the graph contains 630K nodes and 12.8M edges. The distribution of node degree and link strength is shown in Fig. SI1.

By applying our social dimensions classifier to the corpus of messages, we identified the subset of messages that express a social dimension d (see “Methods” for details). In particular, we focused on the dimensions of knowledge exchange and social support (respectively, knowledge and support for short). Other dimensions are discussed in Supplementary Information). The classifier ranked the messages according to their likelihood of containing expressions of a given social dimension; we marked with dimension d only the top 1% of messages from the likelihood ranking of d (we discuss results with looser thresholds in Supplementary Information, Fig. SI2). Out of these smaller sets of messages, we constructed dimension-specific communication graphs $${\mathscr {G}}_d$$ using the same procedure we adopted for building the overall communication graph $${\mathscr {G}}$$. Such dimension-specific graphs capture only one type of social interaction each; for example, the knowledge graph $${\mathscr {G}}_{knowledge}$$ contains only edges formed by knowledge-exchange messages, and edge weights encode the number of knowledge-exchange messages flowing between the two endpoints. The dimension-specific graphs contain roughly $$1\%$$ of the edges of the full communication graph and between 16 to 23% of its nodes, depending on the dimension (see Table 2). The networks of knowledge and support include 20% and 21% of all nodes, respectively. The edges of $${\mathscr {G}}_{knowledge}$$ and $${\mathscr {G}}_{support}$$ overlap only slightly: around 2% of the edges of each graph are also present in the other.

By having a sample of edges annotated with both social dimensions and weight, we were able to look into the relationship between frequency of contacts, knowledge, and support. The typical weight of edges connecting users who exchange knowledge is not dissimilar from the typical weight of those providing support. Figure 1A compares the weight distribution of edges connecting users who exchanged knowledge with the weight distribution of edges connecting those who exchanged support. A two-sample Kolmogorov–Smirnov test (a statistic to measure the distance between two distributions) indicated that the two distributions, albeit statistically different, are very similar: $$KS = 0.03$$ $$(p=0.0)$$ on a range from 0 (indicating identical distributions) to 1 (maximum difference). This comparison exposes the inherent limit of quantifying tie strength with the mere frequency of interactions to adequately qualify the nature of social relationships.

In Reddit conversations, the main difference between knowledge and support ties does not lie in their strength but in their geographic span. The probability of creating knowledge ties increases with the geographical distance between the two endpoints, while the probability of creating support ties drops with distance (Fig. 1B,C). This is consistent with theoretical expectations. Knowledge production on the Web follows Pareto’s law: a restricted number of experts create and spread information to a vast audience12; consequently, knowledge ends up being locally scarce13 and needs to travel longer distances to reach multiple communities. In past studies, a similar pattern was detected for the communications within large corporations, where geographically distant ties were estimated to be more effective conduits for knowledge flow14,15. The opposite trend holds for support. Geographical distance impacts significantly people’s ability to provide both material and emotional support16. Despite computer-mediated communication has grown the opportunities for providing remote support17, people have an innate sense for local attachments and an economic advantage to foster them18, which might be why support appears more rarely in long-distance relationships8.

Last, we tested if dimension-specific graphs are more indicative of economic development than the full communication graph. We did so by borrowing the experimental setup by Eagle et al.7, who studied the network of phone calls among residents of England and measured the spatial and social diversity ($$D_{spatial}$$) for each of nearly 2,000 regional exchanges in the country. $$D_{spatial}$$ captures the diversity of areas that the residents of a given area communicate with, and they found it to be correlated with the Index of Multiple Deprivation—a composite score of social and economic development based on UK census data. They also tested the robustness of their results with an alternative measure of diversity $$D_{social}$$ that captures the diversity of people connected to the residents of a given area. We reproduced Eagle et al.’s experimental setup and ran an Ordinary Least Squares linear regression (OLS) to predict per-capita Gross Domestic Product (GDP) of US states in the year 201719 from the spatial diversity at state-level computed on (i) the full communication graph ($$D_{spatial}$$) and (ii) the two dimension-specific communication graphs ($$D^{knowledge}_{spatial}$$, $$D^{support}_{spatial}$$). Results for $$D_{social}$$ are highly aligned with those for $$D_{spatial}$$, and we discuss them in Supplementary Information. We focused on 44 states for which Reddit penetration is sufficient and aligned with the population distribution (see “Methods”), however we found qualitatively similar results when considering all states (see Supplementary Information, Table SI3). Regressions models with different combinations of social and spatial diversity are presented in Tables SI1 and SI2.

In Table 1 we compare three linear regressions models: one based on population density only (a validated predictor of economic growth20), one using spatial diversity on the full graph with links weighted based on frequency of interaction, and one using the two spatial diversity scores calculated on the graphs of knowledge and support. The model based on the selected social dimensions is 138% more accurate than the density-only baseline, while the model based on the full communication graph is only 15% more accurate. To check whether the difference in performance is due to the selection of knowledge and support ties or just to the smaller sample considered, we ran a regression using a random sample of ties as small as the number of knowledge ties, and obtained the worst fit ($$R^2_{adj}$$ of approximately 0.1, see Supplementary Information).

In the regression model with the social dimensions, the coefficient for knowledge diversity is positive and the one for support diversity is negative. People living in areas characterized by superior economic outcomes access novel information that is not available locally by establishing a diverse set of global interactions, which is in agreement with the weak tie pillar of Granovetter’s theory. Residents of states with highest per-capita GDP draw their social support mostly from local connections, in agreement with the strong tie pillar of the theory. The effect size of knowledge is stronger (almost double) than the effect size of support, which indicates that the process of knowledge exchange is the primary correlate of economic development, and the network of support compounds over it. A linear regression including other social dimensions is discussed in Table SI4, but the interplay between knowledge and support is more predictive than any other combination of dimensions.

## Discussion

In agreement with Granovetter’s theory, we found that economic development at the level of US states is associated to the abundance of global ties that carry factual knowledge and with the abundance of local ties providing social support. This finding is compatible with the established notion of innovation being fueled primarily by novel information flowing from diverse regions of the social network, and secondarily by an adequate support network to favor the re-elaboration of those ideas locally. This perspective enriches the corpus of experimental evidence about the existence of a trade-off between seeking novel information and building tight networks of support13,21,22. We showed that geographical regions generally experience that trade-off but the regions that achieve high economic success are those that have both global outreach of knowledge exchange and local networks of support.

In contrast with a variety of network science studies, we provided evidence that frequency of contacts might not be a good proxy for tie strength: network diversity calculated on a weighted social network is weakly associated to economic development at state level. Moreover, our results challenge the equivalence between weak ties and knowledge flow, at least for the case of Reddit. Interestingly, we found that knowledge and support ties differ in terms of their geographical span, with knowledge ties being far-reaching, and support ties being local.

The ability of measuring directly these two aspects of social interaction that are postulated by Granovetter’s theory to be drivers to innovation enhances the predictive and descriptive power of network models. Strikingly, narrowing down the analysis to a small subset of messages that express either knowledge or support yields a predictive performance that is as much as double of that of models used in previous research that considered only frequency of contacts7.

The ability of decomposing relationship data into interpretable social constituents opens up ample avenues of exploration in social network analysis. Studying how different social dimensions are instantiated by different anatomic patterns of social networks such as their community structure or the centrality of their actors might be a promising research direction. Also, this work showed the association of knowledge and support with GDP, but other social dimensions may well explain other socio-economic outcomes such as health or quality of life.

Both our data and methods suffer from limitations that future work may address. Unlike the work by Eagle et al., upon which our experimental setup was based7, our study relies on social network data that covers only a small sample of the population; this was a necessary sacrifice in order to gain the crucial ability to analyze the content of social interactions.

Within Reddit, our perspective on the ecosystem of social interactions is restricted by our focus on the physical space. In particular, the communication graphs include only a sample of all the existing edges, namely those that connect users whose geo-locations could be estimated. This entails three main biases. First, the majority of interactions are left out of the picture, thus potentially reducing the predictive and descriptive power of our models. Second, the social links we considered were not randomly sampled, as they connect users who self-selected themselves to join geo-salient subreddits. Last, the limited resolution of the user spatial location (state-level) affected our ability to perform a finer-grained geographic analysis (e.g., at city level). To address these biases, future work ought to consider social systems where a larger portion of users can be geo-referenced at a finer geographic resolution.

Even if our social dimensions classifiers were trained on Reddit data and were shown to achieve high accuracy (see “Methods”), their output is not error-free. To improve both precision and recall, a systematic error analysis and a fine-tuning of the model with additional training data would be in order. The ten social dimensions, albeit more comprehensive than any existing model, do not exhaustively map all the possible elements that define social interactions. The concepts that these social dimensions encode are rather broad and encompass a rich spectrum of nuances. The main goal of this work was to go beyond simple frequency of contacts as a proxy for tie strength, offering well-founded interaction archetypes that could be explored and refined in the future.

## Methods

### Reddit data collection

Reddit is a public discussion website particularly popular in the United States where half of its user traffic is generated. Reddit is structured in an ever-growing set of independent subreddits (1.2M at the time of writing) dedicated to a broad range of topics25. Users can post new submissions to any subreddit, and other users can add comments to submissions or to existing comments, thus creating nested conversation threads.

The vast majority of Reddit submissions and comments since 2007 is publicly available through the pushshift.io API41. For the purpose of this study, we gathered the content created in two temporal windows: from 2007 until the end of 2012, and for the whole year of 2017. The findings presented in the “Results” section were obtained using the data from these two windows jointly, but having at hand two collections from distinct time periods allowed us to study how data recency affects the ability to predict the desired outcome (see Supplementary Information, Fig. SI3). In total, we collected 65M comments from 1.3M users.

We restricted our study to users whom we could geo-reference at the level of US States. Although Reddit does not provide explicit information about user location, we used a location-estimation heuristic proven to be effective in previous work42. We first identified 2,844 geo-salient subreddits related to cities or states in the United (https://www.reddit.com/r/LocationReddits/wiki/faq/northamerica). We assigned a user to a state if (i) they posted at least n submissions or comments in subreddits related to that state, and (ii) 95% or more of their comments and submissions posted to geo-salient subreddits were done in subreddits related to that state. The findings presented earlier were obtained with $$n=3$$; in Supplementary Information (Fig. SI4) we discuss results obtained by varying this threshold. Overall, we found 632k users who are likely to be located in one of the 51 US states. The number of users per state ranges from less than 1k (Wyoming) to 61k (California). In total, these users posted 16.2M comments in total (9.8M in 2007–2012, and 6.4 in 2017).

### Filtering states by Reddit penetration

States in which the number of Reddit users is not proportional to the number of residents might distort the representation of social communication patterns that actually take place in those states. To identify such cases, we proceeded as follows. We first plotted the census population in 2017 against the number of Reddit users, across states (Fig. 2, left). We then obtained the best linear fit of the data and calculated the residuals between the number of Reddit users and the predicted value according to the linear fit. Last, we calculated the distribution of residuals and removed states whose residuals were more than 1 standard deviation away from the average of the distribution. Those included two states whose Reddit user base was higher than what one would expect based on their population (DC and AK) and two for which it was lower (MS and WV). In addition, we removed three outlier states whose Reddit penetration was lowest (less than 1000 users), which left us with a total of 44 states (Fig. 2, right).

### Social dimensions from textual conversations

Social science research proposed several categorizations of constitutional sociological dimensions that describe human relationships8,51,52. By surveying such extensive literature, Deri et al.9 compiled one of the most comprehensive categorizations to date, which identifies ten main dimensions of social relationships (Table 2). This theoretical model is rather exhaustive in that most relationships are accurately defined by appropriate combinations of the ten dimensions—Deri et al. showed it by asking hundreds of volunteers to write down keywords that described their relationships and found that all of them fitted into the ten dimensions. The ten social dimensions are frequently expressed through conversational language and, most importantly, these verbal expressions can be captured with computational tools.

We infer the social dimensions from Reddit messages using the NLP model proposed by Choi et al.10, which comes with a publicly-available python implementation (http://www.github.com/lajello/tendimensions). Given a textual message m and a social dimension d, the model estimates the likelihood that m conveys d by giving in output a score from 0 (least likely) to 1 (most likely). Rather than using a multiclass classifier, the model includes ten independently-trained binary classifiers $$C_d$$, one per each dimension. This choice was driven by the theoretical interpretation of the social dimensions9, as any sentence may potentially convey several dimensions at once (e.g., a message expressing both trust and emotional support). Each classifier is implemented using a Long Short-Term Memory neural network (LSTM)53, a type of Recurrent Neural Network (RNN) that is particularly effective in modeling both long and short-range semantic dependencies between words in a text, and it is therefore widely used in a variety of NLP tasks54. Like most RNNs, LSTM accepts fixed-size inputs. This particular model takes in input a 300-dimension embedding vector of a word, one word at a time for all the words in the input text. Embedding vectors are dense numerical representations of the position of a word in a multidimensional semantic space. Such representations are learned from large text corpora. This model uses GloVe embeddings55 learned from Common Crawl, a text corpus containing 840B tokens.

The dimensions classifiers $$C_d$$ were trained using about 9k sentences that were manually labeled by trained crowdsourcing workers. Most of these sentences were taken from Reddit, which makes it the ideal platform to apply the model on. In their experiments, Choi et al. reported very high classification performance which averages to an Area Under the Curve (AUC) of 0.84 across dimensions, and specifically 0.82 for knowledge and 0.83 for support. AUC is a standard performance metric that assesses the ability of a classifier to rank positive and negative instances by their likelihood score, independent of any fixed decision threshold. The AUC of a random classifier is expected to be 0.5, whereas the maximum value is 1.

Given in input a message m, the classifier outputs a score $$s_d(m)$$ that expresses the likelihood that message m contains dimension d. In practice, the classifier estimates a score for each sentence in m and returns the maximum score, namely: $$s_d(m) = \max _{sentence \in m} s_d(sentence)$$. By using the maximum score, we considered a message as likely to express dimension d as its most likely sentence, thus avoiding the dilution effect of the average. This reflects the theoretical interpretation of the use of the social dimensions in language9: a dimension is conveyed effectively through language even when expressed only briefly.

To conduct our analysis, we binarized the classifier scores $$s_d(m)$$ using an indicator function that assigns dimension d to m if $$s_d(m)$$ is above a certain threshold $$\theta _d$$:

\begin{aligned} d(m) = {\left\{ \begin{array}{ll} 1, &{}\quad \text {if } s_d(m) \ge \theta _d\\ 0, &{}\quad \text {otherwise } \end{array}\right. } \end{aligned}
(1)

We used dimension-specific thresholds because the empirical distribution of the classifier scores $$s_d$$ varies noticeably across dimensions (see Fig. 3, left), which makes the use of a fixed common threshold unpractical. We made a very conservative choice of $$\theta _d$$ as the value of the 99th percentile of the distribution of the classifier score $$s_d$$, thus favoring high precision over recall. This effectively reduces the number of messages to 1% of the total and the number of edges to slightly more than 1% of the total. In Supplementary Information (Fig. SI2, right), we experimented with different percentiles, starting from the 75th.

As a result of this procedure, a comment could end up being labeled with multiple dimensions. To measure the extent to which pairs of dimensions are related, we computed the Spearman rank cross-correlation matrix of the classifier scores of all dimension pairs across all messages (Fig. 3, right). Some pairs of dimensions such as status, trust and support occur more frequently together, but overall the ten dimension model exhibits a fairly high degree of orthogonality. To make sure that the ten dimension classifier is not capturing simply the sentiment of the text, we correlated the dimensions scores with the scores from Vader, a simple yet widely-used sentiment analyzer56. The correlations were all very low except for a negative correlation with the conflict dimension.

### Communication graphs

In Reddit, conversations develop over discussion threads. If user i commented over either a submission or a comment of another user j, we considered that i sent a message to j. We created a directed communication graph $${\mathscr {G}}(U,E)$$ to model such exchange of messages. The set of nodes U contains all the geo-referenced users in our sample. We connected two users i and j with a directed edge $$(i, j, w(i, j)) \in E$$ if user i sent at least one message to user j. The edge weight w(ij) represents the ties strength and it is equal to the total number of messages sent. Enforcing a minimum threshold on edge weights for them to be included in the communication graph improved the results, likely because it filters out “occasional” interactions that do not provide a strong signal about the type of social relationships. We used the optimal threshold of $$w(i, j) \ge 4$$; in Supplementary Information (Fig. SI2, left) we present results with different thresholds.

By labeling each message according to the ten social dimensions, we could extract dimension-specific conversation graphs $${\mathscr {G}}_d$$, namely a subgraph of $${\mathscr {G}}$$ created using only the messages that contain dimension d. We built such subgraph using the procedure illustrated in Fig. 4. Given a message m, we computed its classifier score $$s_d(m)$$, which is proportional to the likelihood of m containing expressions of dimension d. We kept only the messages whose likelihood is higher than a dimension-specific threshold: $$s_d(m) \ge \theta _d$$. In practice, we assigned to $$\theta _d$$ the value of the 99th percentile of the empirical distribution of $$s_d(m)$$ values, which effectively retains only $$1\%$$ of the messages. Given such a heavy filtering, we did not enforce a threshold on edge weights. Based on this reduced sets of messages, we constructed a new dimension-specific graph $${\mathscr {G}}(U_d,E_d)$$ that was effectively a subgraph of the original communication graph where an edge $$(i, j, w_d(i, j)) \in E_d$$ encoded the fact that user i sent $$w_d(i, j)$$ messages conveying dimension d to user j. When messages were labeled with multiple dimensions, they contributed equally to multiple dimension-specific subgraphs.

### Computing diversity of interactions

Eagle et al.7 define two measures of diversity: social $$D_{social}$$ and spatial $$D_{spatial}$$. In practice, the two metrics are highly correlated, hence in the main Results we report findings for $$D_{spatial}$$. In Supplementary Information, we discuss findings for both diversity measures.

Given a user i, we first calculated the proportion of the total number of messages that i sent to j, namely:

\begin{aligned} p_{ij} = \frac{w(i,j)}{\sum _{j=1}^{k} w(i,j)}, \end{aligned}
(2)

where k is the total number of i’s social contacts on the communication graph $${\mathscr {G}}$$. In telephone network, the strength of a tie was measured as the total call duration, whereas we measured it as the total number of messages. We then calculated the normalized Shannon entropy of those proportions:

\begin{aligned} D_{social}(i) = \frac{-\sum _{j=1}^{k} p_{ij} \cdot \log (p_{ij})}{\log (k) }. \end{aligned}
(3)

The dimension-specific social diversity was computed with an analogous formula, but taking into account only the edges in the dimension-specific graph $${\mathscr {G}}_d$$:

\begin{aligned} p^d_{ij}= \frac{w_d(i,j)}{\sum _{j=1}^{k_d} w_d(i,j)}, \end{aligned}
(4)
\begin{aligned} D^{d}_{social}(i)= \frac{-\sum _{j=1}^{k_d} p^d_{ij} \cdot \log (p^d_{ij})}{\log (k_d) }, \end{aligned}
(5)

where $$k_d$$ is the total number of i’s social contacts on the dimension-specific graph $${\mathscr {G}}_d$$. To compute the spatial diversity $$D_{spatial}$$, we first calculated the proportion of total volume of messages exchanged by user i with any other users living in area a:

\begin{aligned} p_{ia} = \frac{ \sum _{j \in U_a} w(i,j) }{\sum _{j=1}^{k} w(i,j)}, \end{aligned}
(6)

where A is the total number of areas and $$U_a \subset U$$ is the subset of users living in area a. We then computed the spatial diversity as the normalized entropy of the $$p_{ia}$$ proportions:

\begin{aligned} D_{spatial}(i) = \frac{-\sum _{a=1}^{A} p_{ia} \cdot \log (p_{ia})}{\log (A) }. \end{aligned}
(7)

The same formulation is applied to the dimension-specific graphs:

\begin{aligned} p^{d}_{ia}= \frac{ \sum _{j \in U_a} w_{d}(i,j) }{\sum _{j=1}^{k_d} w_{d}(i,j)}, \end{aligned}
(8)
\begin{aligned} D^{d}_{spatial}(i)= \frac{-\sum _{a=1}^{A} p^{d}_{ia} \cdot \log (p^{d}_{ia})}{\log (A) }. \end{aligned}
(9)

Last, we computed the diversity values at area level by averaging the diversity scores of users living in the same area:

\begin{aligned} D_{social}(a)= \frac{\sum _{i \in U_a} D_{social}(i)}{|U_a|}; D^{d}_{social}(a) = \frac{\sum _{i \in U_a} D^d_{social}(i)}{|U_a|} \end{aligned}
(10)
\begin{aligned} D_{spatial}(a)= \frac{\sum _{i \in U_a} D_{spatial}(i)}{|U_a|}; D^{d}_{spatial}(a) = \frac{\sum _{i \in U_a} D^d_{spatial}(i)}{|U_a|} \end{aligned}
(11)

### Linear regression

Linear regression is an approach for modeling a linear relationship between a dependent variable (GDP, in our experiments) and a set of independent variables (diversity measures), and it does so by associating a so-called $$\beta$$-coefficient with each independent variable such as the sum of all independent variables multiplied by their respective $$\beta$$-coefficients approximates the value of the dependent variable with minimal error. Specifically, we used an Ordinary Least Squares (OLS) regression model to estimate the coefficients such that the sum of the squared residuals between the estimation and the actual value is minimized. The diversity metrics given in input to the regression were approximately normally distributed and bounded in the interval [0,1] (see Fig. SI5)

### Modeling geographical span

To study the dependency between geographical space and social dimensions, we estimated the conditional probability p(d|l) of a dimension d occurring in conversations characterized by a given geographic span (or length) l. Specifically, we considered the set E@l of all edges in the conversation graph $${\mathscr {G}}$$ that connect users at geographic distance l, and the subset of those edges $$E_d@l$$ that belong to the dimension-specific graph $${\mathscr {G}}_d$$. We then computed the conditional probability as the number of dimension-specific edges over the total number of edges at distance l, namely: $$p(d|l) = \frac{|E_d@l|}{|E@l|}$$.

Because activity and connectivity are not uniformly distributed across states, the probability p(d|l) alone could yield a biased view of the interplay between interactions and space. To understand why, consider a scenario in which most of the users are concentrated in one single state. In such a scenario, all users would be constrained to interact mostly with people from that state, and the resulting spatial patterns will be just reflecting the underlying activity and spatial distributions rather than being indicative of explicit user choices. To account for this, we discounted p(d|l) by a probability $$p_{null}(d|l)$$ computed on randomized data. In particular, we generated a random null model by randomly reshuffling the locations across users. By doing so, we preserved both the connectivity properties of the conversation network and the population distribution across states, yet destroying the original relationship between social links and spatial locations. Finally, we computed a normalized score $$\Delta p(d|l) = \frac{p(d|l)}{p_{null}(d|l)} -1$$, which measures the % change of the probability of interaction compared to what it is expected by chance. To obtain the conditional probability associated to individual messages rather than social links, we also computed an alternative version of $$\Delta p(d|l)$$ that considers each message as an individual edge in the graph, thus effectively weighting more pairs of individuals who communicated often.

Since we could geo-reference users at state-level only, we approximated the span of a social link between two users to the length of the straight line connecting the geographic centroids of their states. Given the relatively limited spatial resolution of such a definition, we were bound to a coarse partitioning of distances. Effectively, we divided the set of edges in quintiles based on their geographic span distribution, thus obtaining five equally-sized distance bins, the first of which contains almost exclusively interactions among people in the same state ($$l=0$$).