Social networks have many counter-intuitive properties, including the "friendship paradox" that states, on average, your friends have more friends than you do. Recently, a variety of other paradoxes were demonstrated in online social networks. This paper explores the origins of these network paradoxes. Specifically, we ask whether they arise from mathematical properties of the networks or whether they have a behavioral origin. We show that sampling from heavy-tailed distributions always gives rise to a paradox in the mean, but not the median. We propose a strong form of network paradoxes, based on utilizing the median, and validate it empirically using data from two online social networks. Specifically, we show that for any user the majority of user's friends and followers have more friends, followers, etc. than the user, and that this cannot be explained by statistical properties of sampling. Next, we explore the behavioral origins of the paradoxes by using the shuffle test to remove correlations between node degrees and attributes. We find that paradoxes for the mean persist in the shuffled network, but not for the median. We demonstrate that strong paradoxes arise due to the assortativity of user attributes, including degree, and correlation between degree and attribute.
demonstrated a variety of paradoxes on Twitter beyond the friendship paradox @cite_11 . They showed that users' friends and followers are more active and more highly connected. They claimed that any user attribute correlated with connectivity will ultimately result in a paradox. They don't establish if the activity or virality paradox results simply from the nature of heavy-tailed distributions or from how users choose to position themselves in the network, i.e. behavioral factors. On the other hand, identify some key paradoxes that cannot be explained simply by correlations between degree and activity, such as how overloaded users receive more viral content than underloaded users.
@cite_11
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Feld's friendship paradox states that "your friends have more friends than you, on average." This paradox arises because extremely popular people, despite being rare, are overrepresented when averaging over friends. Using a sample of the Twitter firehose, we confirm that the friendship paradox holds for >98 of Twitter users. Because of the directed nature of the follower graph on Twitter, we are further able to confirm more detailed forms of the friendship paradox: everyone you follow or who follows you has more friends and followers than you. This is likely caused by a correlation we demonstrate between Twitter activity, number of friends, and number of followers. In addition, we discover two new paradoxes: the virality paradox that states "your friends receive more viral content than you, on average," and the activity paradox, which states "your friends are more active than you, on average." The latter paradox is important in regulating online communication. It may result in users having difficulty maintaining optimal incoming information rates, because following additional users causes the volume of incoming tweets to increase super-linearly. While users may compensate for increased information flow by increasing their own activity, users become information overloaded when they receive more information than they are able or willing to process. We compare the average size of cascades that are sent and received by overloaded and underloaded users. And we show that overloaded users post and receive larger cascades and they are poor detector of small cascades. Previous studies have established the link between one's actions (e.g., engaging with others vs. minding one's own business) and one's national culture (e.g., collectivist vs. individualistic), and such actions have been shown to be important as they are collectively affiliated with a country's economic outcomes (e.g., Gross Domestic Product). Hitherto there has not been any systematic study of whether one's action on Twitter (e.g., deciding when to post messages) is linked to one's culture (e.g., country's Pace of Life). To fix that, we build different network snapshots starting from 55,000 seed users on Twitter, and we do so for 10 weeks across 30 countries (after filtering those with low penetration rates) for a total of 2.34 M profiles. Based on Hofstede's theory of cultural dimensions and Levine's Pace of Life theory, we consider three behavioral patterns on Twitter (i.e., temporal predictability of tweets, engaging with others, and supporting others who are less popular) and associate them with three different dimensions derived from the two theories: Pace of Life, Individualism and Power Distance. We find the following strong correlations: activity predictability negatively correlates with Pace of Life (r=-0.62), tweets with mentions negatively correlates with Individualism (r = -0.55), and power (e.g, Twitter popularity) imbalance in relationships (between, for example, two users mentioning each other) is correlated with Power Distance (r=0.62). These three cultural dimensions matter because they are associated with a country's socio-economic aspects - with GDP per capita, income inequality, and education expenditure. Information cascades on social networks, such as retweet cascades on Twitter, have been often viewed as an epidemiological process, with the associated notion of virality to capture popular cascades that spread across the network. The notion of structural virality or average path length has been posited as a measure of global spread. In this paper, we argue that this simple epidemiological view, though analytically compelling, is not the entire story. We first show empirically that the classical SIR diffusion process on the Twitter graph, even with the best possible distribution of infectiousness parameter, cannot explain the nature of observed retweet cascades on Twitter. More specifically, rather than spreading further from the source as the SIR model would predict, many cascades that have several retweets from direct followers, die out quickly beyond that. We show that our empirical observations can be reconciled if we take interests of users and tweets into account. In particular, we consider a model where users have multi-dimensional interests, and connect to other users based on similarity in interests. Tweets are correspondingly labeled with interests, and propagate only in the subgraph of interested users via the SIR process. In this model, interests can be either narrow or broad, with the narrowest interest corresponding to a star graph on the interested users, with the root being the source of the tweet, and the broadest interest spanning the whole graph. We show that if tweets are generated using such a mix of interests, coupled with a varying infectiousness parameter, then we can qualitatively explain our observation that cascades die out much more quickly than is predicted by the SIR model. In the same breath, this model also explains how cascades can have large size, but low "structural virality" or average path length. With the advent of Twitter and other lightweight social-networking services, one might think that it is easier than ever to maintain geographically dispersed, weaker social ties. By contrast, in this study we show that the international Twitter communication landscape is not only still largely predetermined by physical distance, but that it also depends on countries' social, economic, and cultural attributes. We describe a study of an international Twitter mention network of 13 million users across over 100 countries. We show that the Gravity Model, which hypothesizes that the flow between two areas is proportional to their masses (which we approximate using internet penetration) and inversely proportional to the distance between them, is correlated (r=0.68) with the international communication flow. Using this model, along with other social, economic, and cultural variables, we predict the communication volume at Adjusted R2 of @math , with trade, language and racial intolerance especially impacting communication. We discuss the implications of these barriers to communication in the contexts of collaborative work, software design, and recommendation systems.