A tie is a link between two persons in a social network. Here, we analyze tie strength in temporal co-authorship social networks by measuring ties persistence and transformation over time. Surprisingly, most ties tend to perish over time. Also, weak and random ties are more present in real co-authorship networks than bridges and strong ones.
Time is a fundamental factor when characterizing the nature and the strength of
relationships, as acquaintances might become friends and vice-versa. Such
timevarying ties may be modeled as a temporal social network (SN), or temporal
graph, where each node is a person and an edge connects two nodes in time t if
they share any relationship at t. However, most studies focus on static aggregated
graphs [
Nonetheless, computing temporal SNs properties and their time-varying
behavior is very challenging, as their values evolve. Hence, concepts and metrics
to analyze static networks must be adapted and extended to time-varying
networks. Tie strength (a.k.a. strength of the ties) is one of those concepts, which
is originally defined as a merge of the time of relationship, the emotional force,
the intimacy, and the reciprocal services that link (through a tie) people [
Here, our goal is to verify if current definitions of tie strength hold for
temporal networks. To do so, we analyze the dynamism of tie strength by observing
link persistence and link transformation over time. This goal is divided in two
research questions. First, how is tie strength defined for temporal networks? We
consider a strong tie characterizes interactions likely to appear in the future,
whereas a weak tie occurs sporadically. Second, how much does tie strength vary
over time? Nicosia et al. [
# nodes # edges D. Articles D. Inproceedings PubMed APS of edge persistence and topological overlap1. These properties represent the regularity of interaction and the similarity between people in a relationship. 2
In order to proceed, we first need to formally define a model for temporal social networks. Therefore, we associate a start time and a duration to each coauthorship. Then, a temporal co-authorship social network is modeled as a graph Gk(Vk; Ek) in which time is discretized into steps of duration 2, and k is the time step in which a co-authorship (encounter) occurs. The set of nodes Vk is formed by all network nodes in a co-authorship during the k-th time step, and the set of edges Ek is composed of co-authorships during the same time step. A timevarying representation of the SNs can be defined by a temporal accumulation graph Gt(Vt; Et), where Gt = G1 [ G2 [ ::: [ Gt, in which t is the last time step. Then, Vt and Et are the set of all nodes and edges in the SNs, respectively, in the time step 0 to t. Since Gt accumulates all co-authorships from the datasets and evolves over time, such aggregate graph contains social and random encounters. Thus, a random version GtR of the temporal aggregated graph Gt is necessary to analyze the patterns of such SN. For this model to work, it requires a definition of tie strength in temporal SNs and an algorithm that implements it. Definition of tie strength. Given a temporal graph Gk(Vk; Ek), where k is the time step in which a co-authorship occurs, a tie (i; j) is likely to be strong if it is present in Gk for most values of k. On the other hand, the tie (i; j) is likely to be weak if it is present in Gk for just a few values of k.
Implementation of the algorithm. One contribution of this work is to modify
an existing algorithm called RECAST [
Then, we propose to apply a multiprocessing Pool module from Python3 in such step of RECAST in order to reduce its complexity. We call this novel, multiprocessing algorithm as fast-RECAST. The idea is that more than one random event graph GtR is built at a time in a multi-core computer. Thus, the new computational cost is O( pt (jVtj+jEtRj)), where p is the number of processes. We also add a multiprocessing Pool module from Python to call the functions to compute the edge persistence and topological overlap from the aggregated graphs. Both features are computed in parallel and asynchronously. Dataset. To analyze tie strength persistence and transformation, we consider three publication datasets: DBLP, PubMed and APS, as collected in September 2015, April 2016 and March 2016, respectively. Considering these datasets, we build four co-authorship SNs whose main statistics are in Table 1. Time Performance. In order to show that fast-RECAST performs better than RECAST, we measure the execution time of both algorithms in a laptop with 8 GB 1600 MHz DDR3 of memory and 2.5 GHz Intel two Core i5 of processor. The operation system is Mac OS X El Capitan version 10.11.6. Figure 1 presents the execution time in seconds of fast-RECAST and RECAST. Note that we present the results only for PubMed dataset, because it is the largest one. Tie strength persistence results. In order to analyze the persistence over time, we divide the networks into two time windows, which from now on we call past and future4. We apply fast-RECAST in the past and then, verify if the edges of each class (strong, bridge, weak and random) continue to be in that same class in the future. To do that, we split the networks into two time windows and in two ways. First, we split the networks into a time window comprising 80% of the initial timestamp (past ) and a time window comprising 20% of the final timestamp (future). Second, we divide the networks into time windows of 70% (past ) and 30% (future). For both 80-20% and 70-30%, strong ties and bridges tend to persist over the years more than weak and random ties. Moreover, we emphasize the differences in the results of the APS network in the 80%-20% and 70%-30% partitions. In the first partitioning, the proportion of strong and bridge ties from the past to the present is very high, whereas in the second partitioning such proportion is lower. This result may indicate that the co-authorship social network from APS changes more through the years than the other networks. Another possibility is that physics researchers do not change very much the level of co-authorship with their collaborators over time, and this is a pattern of more recent researchers (note that 80% of data consider more recent co-authorships than 70%). We leave for future work further analyses of such insights. Tie strength transformation results. We now evaluate the amount of ties from a class in the past that continues in the same class (or changes) in the future, i.e, tie strength transformation analyses. To avoid any kind of bias in the process of classifying the edges, here we divide the temporal co-authorship social net3 Multiprocessing with python:
multiprocessing.html
4 One may see the present as the timestamp between these two time windows
docs.python.org/2/library/
works into two time windows of 50% of the timestamp. We apply fast-RECAST
in both parts and then we analyze the link transformation through the classes.
Surprisingly, we cannot see ties classified as weak and random in DBLP articles
and DBLP Inproceedings. This indicates that the features (edge persistence and
topological overlap) of these social networks have high (or social ) values.
Furthermore, most ties from the past tend to disappear in the present, especially
the bridges. This result may be explained by the nature of co-authorships, as
researchers collaborate during a period towards a common goal and then, start
to collaborate with others. This also reinforces the theory of Granovetter that
weak ties are the ones that connect different communities [
We analyzed ties strength dynamism in temporal SNs. We built four temporal co-authorship SNs considering three real publications datasets, and proposed fast-RECAST, a parallel version of an existing tie classification method. The resulting link persistence analysis reveals that strong ties and bridges tend to persist more than weak and random ties. This supports our hypothesis that strong ties persist more than others. The results also show a different pattern for APS when the data is divided in 80% and 20%. In this experimental setting, the proportion of strong and bridge ties from the past to the present is very high compared to other SN. Also, the link transformation analysis revealed most ties tend to disappear over time. As future work, we plan to investigate the patterns discovered here and to modify fast-RECAST to better capture tie strength. Acknowledgements to CAPES, CNPq and FAPEMIG, Brazil.