The Role of Trends in Evolving Networks

Modeling complex networks has been the focus of much research for over a decade [1]–[3]. Preferential attachment (PA) [4] is considered a common explanation to the self organization of evolving networks, suggesting that new nodes prefer to attach to more popular nodes. The PA model results in broad degree distributions, found in many networks, but cannot explain other common properties such as: The growth of nodes arriving late [5] and Clustering (community structure). Here we show that when the tendency of networks to adhere to trends is incorporated into the PA model, it can produce networks with such properties. Namely, in trending networks, newly arriving nodes may become central at random, forming new clusters. In particular, we show that when the network is young it is more susceptible to trends, but even older networks may have trendy new nodes that become central in their structure. Alternatively, networks can be seen as composed of two parts: static, governed by a power law degree distribution, and a dynamic part governed by trends, as we show on Wiki pages. Our results also show that the arrival of trending new nodes not only creates new clusters, but also has an effect on the relative importance and centrality of all other nodes in the network. This can explain a variety of real world networks in economics, social and online networks, and cultural networks. Products popularity, formed by the network of people’s opinions, exhibit these properties. Some lines of products are increasingly susceptible to trends and hence to shifts in popularity, while others are less trendy and hence more stable. We believe that our findings have a big impact on our understanding of real networks. Trends are a driving force in our lives. From economy to online engagement and popular research subjects, trends govern many aspects [6]–[9]. Trends start locally [10], [11], but only some of them, with time, create enough buzz to accumulate a global effect. We can think, for example, on a giant search engine that has started locally in the academic community at first. Alternatively, there is a popular recent Korean clip, that managed to become the number one hit on YouTube of all times1. We suggest that the preferential attachment process needs to be expanded to include the tendency of new and existing nodes to connect not only to rich nodes, but also to trending nodes. Hence, a node is attractive if it is either rich or trendy, and