Centrality metric for dynamic networks

Abstract

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.

Random walks on temporal networks

“…Our investigations also open interesting directions for future work. For instance, it would be interesting to investigate how random walks starting from different nodes explore first their own neighborhood [47], which might lead to hints about the definition of "temporal communities" (see, e.g., [48] for an algorithm using RW on static networks for the detection of static communities); various measures of node centrality have also been defined in temporal networks [1,44,[49][50][51], but their computation is rather heavy, and RW processes might present interesting alternatives, similarly to the case of static networks [52].…”

GraphDiaries: Animated Transitions andTemporal Navigation for Dynamic Networks

“…However, this method makes it hard to encode other temporal measures such as the time between two connections in a node pair or particular network-specific attributes such as node type. Values are often aggregated and the goal is to provide a single measure to describe the entire dynamic behavior [9][10], thereby omitting information about the individual time points. A single image enhanced with explicit encoding of temporal changes also increases the visual complexity of the network representation, and important temporal information can get lost if not encoded explicitly.…”

“…We use halos to highlight changing nodes and edges rather than coloring them directly, so as to avoid interfering with existing visual encodings (D2), instead making it possible to visually encode, for example, temporal network measurements such as dynamic centrality, or domain-specific data attributes [9][10]. Figure 1 shows that halos are still visible when node fill color encodes a domain-specific data attribute.…”

Visual Analysis of Dynamic Networks Using Change Centrality

“…The time-scale degree centrality has been defined as an extension of the static degree centrality that takes into account both the presence and duration of links [11]. Lerman et al [12] introduce an attenuation factor to the link duration and on this basis define a centrality metric for dynamic networks. By modelling social interactions as temporal events and taking into account when they occur, Berger-Wolf and Saia [13] introduce a framework consisting of several metrics for the analysis of dynamic social networks.…”