Visual analysis of temporal networks comprises an effective way to understand the network dynamics, facilitating the identification of patterns, anomalies, and other network properties, thus resulting in fast decision making. The amount of data in real-world networks, however, may result in a layout with high visual clutter due to edge overlapping. This is particularly relevant in the so-called streaming networks, in which edges are continuously arriving (online) and in non-stationary distribution. All three network dimensions, namely node, edge, and time, can be manipulated to reduce such clutter and improve readability. This paper presents an online and nonuniform timeslicing method, thus considering the underlying network structure and addressing streaming network analyses. We conducted experiments using two real-world networks to compare our method against uniform and nonuniform timeslicing strategies. The results show that our method automatically selects timeslices that effectively reduce visual clutter in periods with bursts of events. As a consequence, decision making based on the identification of global temporal patterns becomes faster and more reliable.