# DyEgoVis: Visual Exploration of Dynamic Ego-Network Evolution
## 1 Introduction  
Networks (a.k.a. graphs) are ubiquitous data that can be used to model relationships between entities such as communications between e-mails, partnerships between companies, friendships between Facebook users, and interactions between proteins. Real-world networks are often dynamic. Their topology or node/edge attributes change over time. Due to the extra time dimension, analyzing dynamic networks becomes a challenging task. Based on different analysis perspectives, dynamic network analysis can be divided into whole-network analysis and egocentric analysis [1]. The former displays the structure of the entire dynamic network to reveal global evolution patterns such as cluster formation and separation. Different from the former, the latter focuses on a local sub-network centered on a focus node and analyzes its evolutionary process. Formally, this sub-network is called an ego-network which consists of a focus node (called ego), its neighbors (called alters), and all the connections among these nodes. In an ego-network, its ego's k-hop neighbors are called k-level alters. For ego-network analysis, only one-level and two-level alters are usually considered [2]. In a dynamic network, each node has its own ego-network sequence known as a dynamic ego-network. In this paper, the static ego-network of a dynamic ego-network at a timestep is called a snapshot. A snapshot is actually an evolution state of the dynamic ego-network at the timestep. Egocentric analysis of a dynamic network is to explore the evolutions of its dynamic ego-networks, which can help users gain insight into how each ego interacts with and is influenced by the outside world. For instance, telecommunication analysts can identify spammer behaviors by the daily communications between an ego and alters [3]; academic analysts can analyze a scholar's academic career through the scholar's collaboration networks over the years [4]; and sociologists can infer an individual's behavior patterns by investigating whether the individual's social network grows continuously or changes suddenly [5]. As the most natural method of data analysis, visualization can help users efficiently explore the evolutions of dynamic ego-networks and discover hidden evolution patterns. We should explore the evolutions of dynamic ego-networks in a dynamic network at three different analysis levels derived from the visual information seeking mantra \"overview, zoom and filter, details-on-demand\" [6]. At the global level, we should summarize the evolution patterns of all the dynamic ego-networks to find similar or uncommon evolution patterns. At the local level, we should compare the selected dynamic ego-networks' states (snapshots) to identify similar or abnormal states. At the individual level, we should compare and analyze the evolution of each selected dynamic ego-network. For example, how does the number of alters change over time; how long does the specified ego-alter relationship last; and can a two-level alter become a one-level alter over time? Although many methods have been proposed for the visual exploration of dynamic networks [7], they mainly focus on visualizing the whole dynamic network rather than its dynamic ego-networks. More and more studies focus on exploring dynamic ego-networks, but most of them do not fully consider the above three analysis levels, resulting in some information at different granularities being omitted. In this paper, we focus on the multilevel analysis of dynamic ego-networks. To this end, we propose DyEgoVis, an interactive visualization system that allows users to explore the evolutions of dynamic ego-networks at the three analysis levels. Based on an ego-network embedding model, the system reduces both dynamic ego-networks and their snapshots to 2D points, thereby overviewing the evolution patterns of dynamic ego-networks for the global-level analysis. Clusters of points reveal similar evolution patterns while outlier points indicate abnormal evolution patterns.