Datasets are often collected through surveys or interviews at a single point in time. Consequently, the evolution of networks is typically not recorded (i.e., static). As such, most network measures have been developed for the purpose of analysing cross-sectional networks. However, for certain types of analyses, knowing the evolution is key. This is particularly the case when studying tie formation in networks. In a static network, it is not appropriate to model the existence of ties based the neighbouring ties as ties are not independent of each other. In fact, the network is a reflection of the dependency structure. One way to overcome this obstacle is to employ highly complex simulations to infer the likelihood of tie formation based on structural configurations (Robins and Morris, 2007). Another approach is to observe the network at multiple times and simulating the changes between panels using stochastic actor-oriented models (SAOMs; Snijders, 1996, 2001). This latter approach has allowed for studies of both selection and influence in social networks, and thereby, giving insights into whether behavioral process emerge from or contribute to network formation. One known limitation of SAOMs is that they infer continuous time process as it only observes discrete snapshots of the network.
In recent years, there has been a growing use of networks where the time of tie creation is recorded (Brandes et al., 2009; Butts, 2008; de Nooy, 2011; Kossinets and Watts, 2006; Opsahl and Hogan, 2011; Stadtfeld, 2010). These networks are often referred to as relational event, timestamped, continuously-observed, or longitudinal networks. There are multiple types of longitudinal networks. They might be one-mode or two-mode, binary or weighted, have time information for ties only or also for nodes, and information of tie creation/reinforcement but not on weakening/severing. Read more…
A common way of analysing richer types of networks is to create static snapshots at a fixed interval (e.g., daily, weekly, or yearly; Kossinets and Watts, 2006; Panzarasa et al., 2009). This process generates insights into how network properties change over time, such as the average degree or clustering coefficient. A key benefit of this approach is that any static network measure can be applied to the network. This page shows how to apply some common network measures. Read more…
Many longitudinal networks are collected using archival data. These datasets often do not contain information on the weakening and severing of ties. If this is the case and the network is analysed directly, there is an assumption that relationships, once established, never decay. This can be overcome by introducing a sliding window that removes ties after a set amount of time (Kossinets and Watts, 2006; Panzarasa et al., 2009). The length of the window is crucial in determining which past events are taken into account to generate the network structure at a given point in time. By analysing which past events are relevant to the current state of the network, the length of the window can be defined. An ill-defined sliding window will have the effect of, either breaking continuous social interactions into independent sets of interactions, or combining two separate interactions into a single one. Read more…
Understanding how networks evolve has been a quest in network analysis. However, static network data is far from ideal when trying to achieve this goal. It is first with longitudinal data that we are able to detect the underpinning principles of tie formation in large-scale networks. In recent years, a number of frameworks has been developed for various types of longitudinal data (Brandes et al., 2009; Butts, 2008; de Nooy, 2011; Kossinets and Watts, 2006; Opsahl and Hogan, 2011; Stadtfeld, 2010). Although this page will focus on my work in this field (Opsahl and Hogan, 2011), it will try to include the other frameworks were applicable. Read more…
Random Longitudinal Networks
Similarly to weighted networks and two-mode networks, random networks play an important role when analysing longitudinal networks. After estimating growth parameters on an observed networks, it is possible to create random networks based on these parameters and then test whether the random networks resemble the observed networks. This would be similar to goodness-of-fit for SIENA models. Read more…
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