Complex networks often exhibit co-evolutionary dynamics, meaning that the network topology and the state of nodes or links are coupled, affecting each other in overlapping time scales. We focus on the co-evolutionary dynamics of online social networks, and on Twitter in particular. Monitoring the activity of thousands of Twitter users in real-time, and tracking their followers and tweets/retweets, we propose a method to infer new retweet-driven follower relations. The formation of such relations is much more likely than the exogenous creation of new followers in the absence of any retweets. We identify the most significant factors (reciprocity and the number of retweets that a potential new follower receives) and propose a simple probabilistic model of this effect. We also discuss the implications of such co-evolutionary dynamics on the topology and function of a social network. Finally, we briefly consider a second instance of co-evolutionary dynamics on Twitter, namely the possibility that a user removes a follower link after receiving a tweet or retweet from the corresponding followee.

Abstract

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Complex networks often exhibit co-evolutionary dynamics, meaning that the network topology and the state of nodes or links are coupled, affecting each other in overlapping time scales. We focus on the co-evolutionary dynamics of online social networks, and on Twitter in particular. Monitoring the activity of thousands of Twitter users in real-time, and tracking their followers and tweets/retweets, we propose a method to infer new retweet-driven follower relations. The formation of such relations is much more likely than the exogenous creation of new followers in the absence of any retweets. We identify the most significant factors (reciprocity and the number of retweets that a potential new follower receives) and propose a simple probabilistic model of this effect. We also discuss the implications of such co-evolutionary dynamics on the topology and function of a social network.Online Social Networks (OSNs), such as Twitter and Facebook, have changed how individuals interact with society, how information flows between actors, and how people influence each other. These are all complex dynamic processes that are now widely studied empirically and in large scale, thanks to the availability of data from OSNs. Most OSN studies focus on one of the following two aspects of network dynamics. Dynamics on networks refer to changes in the state of network nodes or links considering a static topology [1,2]. Dynamics of networks, on the other hand, refer to changes in the topology of a network, without explicitly modeling its underlying causes [3]. As noted by Gross and Blasius in [4], however, real OSNs typically exhibit both types of dynamics, forming an adaptive, or co-evolutionary, system in which the network topology and the state of nodes/links affect each other through a (rather poorly understood) feedback loop.Dynamic processes in OSNs, such as information diffusion or influence, are obviously affected by the underlying network topology, but they also have the power to affect that topology. For instance, users may decide to add or drop a "friendship" or "follower" relation depending on what the potential "friend" or "followee" has recently said or done in the context of that OSN. Previous empirical or modeling OSN studies often choose to ignore such co-evolutionary dynamics, mostly for simplicity, assuming a static network topology, or assuming that the topology and node/link states are decoupled and evolve in separate time scales [5].The literature on co-evolutionary dynamics has relied mostly on abstract models so far, without sufficient empirical validation. For instance, Kosma and Barrat examined how the topology of an adaptive network of interacting agents and of the agents' opinions can influence each other [6]. When agents rewire their links in a way that depends on the opinions of their neighbors, the result can be either a large number of small clusters, making global consensus difficult, or a highly connected but polarized network. Shaw and Schwartz [7] examined the effects of vaccination in static ...