Did they represent tie strength only as number of social ties in a networks? 
Yes, a normalized mutual friends metric
Language change is a complex social phenomenon, revealing pathways of communication and sociocultural influence. But, while language change has long been a topic of study in sociolinguistics, traditional linguistic research methods rely on circumstantial evidence, estimating the direction of change from differences between older and younger speakers. In this paper, we use a data set of several million Twitter users to track language changes in progress. First, we show that language change can be viewed as a form of social influence: we observe complex contagion for phonetic spellings and"netspeak"abbreviations (e.g., lol), but not for older dialect markers from spoken language. Next, we test whether specific types of social network connections are more influential than others, using a parametric Hawkes process model. We find that tie strength plays an important role: densely embedded social ties are significantly better conduits of linguistic influence. Geographic locality appears to play a more limited role: we find relatively little evidence to support the hypothesis that individuals are more influenced by geographically local social ties, even in their usage of geographical dialect markers.
Change is a universal property of language. For example, English has changed so much that Renaissance-era texts like The Canterbury Tales must now be read in translation. Even contemporary American English continues to change and diversify at a rapid pace—to such an extent that some geographical dialect differences pose serious challenges for comprehensibility BIBREF0 . Understanding language change is therefore crucial to understanding language itself, and has implications for the design of more robust natural language processing systems BIBREF1 . Language change is a fundamentally social phenomenon BIBREF2 . For a new linguistic form to succeed, at least two things must happen: first, speakers (and writers) must come into contact with the new form; second, they must decide to use it. The first condition implies that language change is related to the structure of social networks. If a significant number of speakers are isolated from a potential change, then they are unlikely to adopt it BIBREF3 . But mere exposure is not sufficient—we are all exposed to language varieties that are different from our own, yet we nonetheless do not adopt them in our own speech and writing. For example, in the United States, many African American speakers maintain a distinct dialect, despite being immersed in a linguistic environment that differs in many important respects BIBREF4 , BIBREF5 . Researchers have made a similar argument for socioeconomic language differences in Britain BIBREF6 . In at least some cases, these differences reflect questions of identity: because language is a key constituent in the social construction of group identity, individuals must make strategic choices when deciding whether to adopt new linguistic forms BIBREF7 , BIBREF8 , BIBREF9 . By analyzing patterns of language change, we can learn more about the latent structure of social organization: to whom people talk, and how they see themselves. But, while the basic outline of the interaction between language change and social structure is understood, the fine details are still missing: What types of social network connections are most important for language change? To what extent do considerations of identity affect linguistic differences, particularly in an online context? Traditional sociolinguistic approaches lack the data and the methods for asking such detailed questions about language variation and change. In this paper, we show that large-scale social media data can shed new light on how language changes propagate through social networks. We use a data set of Twitter users that contains all public messages for several million accounts, augmented with social network and geolocation metadata. This data set makes it possible to track, and potentially explain, every usage of a linguistic variable as it spreads through social media. Overall, we make the following contributions: