The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is known today about the network dynamics: indeed, complex networks in reality are not static, but rather dynamically evolve over time. Our paper is motivated by the empirical observation that network evolution patterns seem far from random, but exhibit structure. Moreover, the specific patterns appear to depend on the network type, contradicting the existence of a " one fits it all " model. However, we still lack observables to quantify these intuitions, as well as metrics to compare graph evolutions. Such observables and metrics are needed for extrapolating or predicting evolutions, as well as for interpolating graph evolutions. To explore the many faces of graph dynamics and to quantify temporal changes, this paper suggests to build upon the concept of centrality, a measure of node importance in a network. In particular, we introduce the notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type. Intuitively, centrality distances reflect the extent to which (non-anonymous) node roles are different or, in case of dynamic graphs, have changed over time, between two graphs. We evaluate the centrality distance approach for five evolutionary models and seven real-world social and physical networks. Our results empirically show the usefulness of centrality distances for characterizing graph dynamics compared to a null-model of random evolution, and highlight the differences between the considered scenarios. Interestingly, our approach allows us to compare the dynamics of very different networks, in terms of scale and evolution speed.
Many networks are dynamic in that their topology changes rapidly—on the same time scale as the communications of interest between network nodes. Examples are the human contact networks involved in the transmission of disease, ad hoc radio networks between moving vehicles, and the transactions between principals in a market. While we have good models of static networks, so far these have been lacking for the dynamic case. In this paper we present a simple but powerful model, the time-ordered graph, which reduces a dynamic network to a static network with directed flows. This enables us to extend network properties such as vertex degree, closeness, and betweenness centrality metrics in a very natural way to the dynamic case. We then demonstrate how our model applies to a number of interesting edge cases, such as where the network connectivity depends on a small number of highly mobile vertices or edges, and show that our centrality definition allows us to track the evolution of connectivity. Finally we apply our model and techniques to two real-world dynamic graphs of human contact networks and then discuss the implication of temporal centrality metrics in the real world. Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to static networks. Most networks, on the other hand, are dynamic in nature, evolving over time through the addition or deletion of nodes and edges. A popular approach to analyzing such networks represents them by a static network that aggregates all edges observed over some time period. This approach, however, under or overestimates centrality of some nodes. We address this problem by introducing a novel centrality metric for dynamic network analysis. This metric exploits an intuition that in order for one node in a dynamic network to influence another over some period of time, there must exist a path that connects the source and destination nodes through intermediaries at different times. We demonstrate on an example network that the proposed metric leads to a very different ranking than analysis of an equivalent static network. We use dynamic centrality to study a dynamic citations network and contrast results to those reached by static network analysis. There is an ever-increasing interest in investigating dynamics in time-varying graphs (TVGs). Nevertheless, so far, the notion of centrality in TVG scenarios usually refers to metrics that assess the relative importance of nodes along the temporal evolution of the dynamic complex network. For some TVG scenarios, however, more important than identifying the central nodes under a given node centrality definition is identifying the key time instants for taking certain actions. In this paper, we thus introduce and investigate the notion of time centrality in TVGs. Analogously to node centrality, time centrality evaluates the relative importance of time instants in dynamic complex networks. In this context, we present two time centrality metrics related to diffusion processes. We evaluate the two defined metrics using both a real-world dataset representing an in-person contact dynamic network and a synthetically generated randomized TVG. We validate the concept of time centrality showing that diffusion starting at the best ranked time instants (i.e., the most central ones), according to our metrics, can perform a faster and more efficient diffusion process. The article introduces the concept of snapshot dynamic indices as centrality measures to analyse how the importance of nodes changes over time in dynamic networks. In particular, the dynamic stress-snapshot and dynamic betweenness snapshot are investigated. We present theoretical results on dynamic shortest paths in first-in first-out dynamic networks, and then introduce some algorithms for computing these indices in the discrete-time case. Finally, we present some experimental results exploring the algorithms' efficiency and illustrating the variation of the dynamic betweenness snapshot index for some sample dynamic networks.