Negative or antagonistic relationships are common in human social networks, but they are less often studied than positive or friendly relationships. The existence of a capacity to have and to track antagonistic ties raises the possibility that they may serve a useful function in human groups. Here, we analyze empirical data gathered from 24,770 and 22,513 individuals in 176 rural villages in Honduras in two survey waves 2.5 y apart in order to evaluate the possible relevance of antagonistic relationships for broader network phenomena. We find that the small-world effect is more significant in a positive world with negative ties compared to an otherwise similar hypothetical positive world without them. Additionally, we observe that nodes with more negative ties tend to be located near network bridges, with lower clustering coefficients, higher betweenness centralities, and shorter average distances to other nodes in the network. Positive connections tend to have a more localized distribution, while negative connections are more globally dispersed within the networks. Analysis of the possible impact of such negative ties on dynamic processes reveals that, remarkably, negative connections can facilitate the dissemination of information (including novel information experimentally introduced into these villages) to the same degree as positive connections, and that they can also play a role in mitigating idea polarization within village networks. Antagonistic ties hold considerable importance in shaping the structure and function of social networks.

In recent years, critics of online platforms have raised concerns about the ability of recommendation algorithms to amplify problematic content, with potentially radicalizing consequences. However, attempts to evaluate the effect of recommenders have suffered from a lack of appropriate counterfactuals – what a user would have viewed in the absence of algorithmic recommendations – and hence cannot disentangle the effects of the algorithm from a user’s intentions. Here we propose a method that we call "counterfactual bots" to causally estimate the role of algorithmic recommendations on the consumption of highly partisan content. By comparing bots that replicate real users’ consumption patterns with "counterfactual" bots that follow rule-based trajectories, we show that, on average, relying exclusively on the recommender results in less partisan consumption, where the effect is most pronounced for heavy partisan consumers. Following a similar method, we also show that if partisan consumers switch to moderate content, YouTube’s sidebar recommender "forgets" their partisan preference within roughly 30 videos regardless of their prior history, while homepage recommendations shift more gradually towards moderate content. Overall, our findings indicate that, at least on YouTube, individual consumption patterns mostly reflect individual preferences, where algorithmic recommendations play, if anything, a moderating role.

The "friendship paradox" of social networks states that, on average, "your friends have more friends than you do." Here, we theoretically and empirically explore a related and overlooked paradox we refer to as the "enmity paradox." We use empirical data from 24,687 people living in 176 villages in rural Honduras. We show that, for a real negative undirected network (created by symmetrizing antagonistic interactions), the paradox exists as it does in the positive world. Specifically, a person’s enemies have more enemies, on average, than a person does. Furthermore, in a mixed world of positive and negative ties, we study the conditions for the existence of the paradox, both theoretically and empirically, finding that, for instance, a person’s friends typically have more enemies than a person does. We also confirm the "generalized" enmity paradox for nontopological attributes in real data, analogous to the generalized friendship paradox (e.g., the claim that a person’s enemies are richer, on average, than a person is). As a consequence, the naturally occurring variance in the degree distribution of both friendship and antagonism in social networks can skew people’s perceptions of the social world.

Although it is under-studied relative to other social media platforms, YouTube is arguably the largest and most engaging online media consumption platform in the world. Recently, YouTube’s scale has fueled concerns that YouTube users are being radicalized via a combination of biased recommendations and ostensibly apolitical “anti-woke” channels, both of which have been claimed to direct attention to radical political content. Here we test this hypothesis using a representative panel of more than 300,000 Americans and their individual-level browsing behavior, on and off YouTube, from January 2016 through December 2019. Using a labeled set of political news channels, we find that news consumption on YouTube is dominated by mainstream and largely centrist sources. Consumers of far-right content, while more engaged than average, represent a small and stable percentage of news consumers. However, consumption of “anti-woke” content, defined in terms of its opposition to progressive intellectual and political agendas, grew steadily in popularity and is correlated with consumption of far-right content off-platform. We find no evidence that engagement with far-right content is caused by YouTube recommendations systematically, nor do we find clear evidence that anti-woke channels serve as a gateway to the far right. Rather, consumption of political content on YouTube appears to reflect individual preferences that extend across the web as a whole.

Most real-world networks are incompletely observed. Algorithms that can accurately predict which links are missing can dramatically speed up network data collection and improve network model validation. Many algorithms now exist for predicting missing links, given a partially observed network, but it has remained unknown whether a single best predictor exists, how link predictability varies across methods and networks from different domains, and how close to optimality current methods are. We answer these questions by systematically evaluating 203 individual link predictor algorithms, representing three popular families of methods, applied to a large corpus of 550 structurally diverse networks from six scientific domains. We first show that individual algorithms exhibit a broad diversity of prediction errors, such that no one predictor or family is best, or worst, across all realistic inputs. We then exploit this diversity using network-based metalearning to construct a series of “stacked” models that combine predictors into a single algorithm. Applied to a broad range of synthetic networks, for which we may analytically calculate optimal performance, these stacked models achieve optimal or nearly optimal levels of accuracy. Applied to real-world networks, stacked models are superior, but their accuracy varies strongly by domain, suggesting that link prediction may be fundamentally easier in social networks than in biological or technological networks. These results indicate that the state of the art for link prediction comes from combining individual algorithms, which can achieve nearly optimal predictions. We close with a brief discussion of limitations and opportunities for further improvements.

A common graph mining task is community detection, which seeks an unsupervised decomposition of a network into groups based on statistical regularities in network connectivity. Although many such algorithms exist, community detection’s No Free Lunch theorem implies that no algorithm can be optimal across all inputs. However, little is known in practice about how different algorithms over or underfit to real networks, or how to reliably assess such behavior across algorithms. Here, we present a broad investigation of over and underfitting across 16 state-of-the-art community detection algorithms applied to a novel benchmark corpus of 572 structurally diverse real-world networks. We find that (i) algorithms vary widely in the number and composition of communities they find, given the same input; (ii) algorithms can be clustered into distinct high-level groups based on similarities of their outputs on real-world networks; (iii) algorithmic differences induce wide variation in accuracy on link-based learning tasks; and, (iv) no algorithm is always the best at such tasks across all inputs. Finally, we quantify each algorithm’s overall tendency to over or underfit to network data using a theoretically principled diagnostic, and discuss the implications for future advances in community detection.

The detection of communities within a dynamic network is a common means for obtaining a coarse-grained view of a complex system and for investigating its underlying processes. While a number of methods have been proposed in the machine learning and physics literature, we lack a theoretical analysis of their strengths and weaknesses, or of the ultimate limits on when communities can be detected. Here, we study the fundamental limits of detecting community structure in dynamic networks. Specifically, we analyze the limits of detectability for a dynamic stochastic block model where nodes change their community memberships over time, but where edges are generated independently at each time step. Using the cavity method, we derive a precise detectability threshold as a function of the rate of change and the strength of the communities. Below this sharp threshold, we claim that no efficient algorithm can identify the communities better than chance. We then give two algorithms that are optimal in the sense that they succeed all the way down to this threshold. The first uses belief propagation, which gives asymptotically optimal accuracy, and the second is a fast spectral clustering algorithm, based on linearizing the belief propagation equations. These results extend our understanding of the limits of community detection in an important direction, and introduce new mathematical tools for similar extensions to networks with other types of auxiliary information.