Exploring the transition behavior of nodes in temporal networks based on dynamic community detection

Highlights

• Experiments on 15 real-world dynamic networks to explore the transition behavior of nodes.

• Using the decision tree to find the node-level features that have a general impact on node transition.

• Average neighbor degree and node’s degree are the more important features in this study.

• We also find some interesting phenomena in real dynamic networks.

Abstract

Community detection and community evolution tracking are two important tasks in dynamic complex network analysis. Recently, a variety of models and methods have been proposed for detecting the community structure and analyzing their evolution. However, all these methods are only committed to improving the performance of community detection or identifying evolutionary events, ignoring the internal relevance between the structure of each snapshot of the dynamic network and the evolution pattern of communities, especially the structural features of nodes and their dynamic transition behavior. To cope with this problem, we firstly conduct experiments on 15 real-world dynamic networks to explore the transition behavior of nodes in dynamic networks, which is one of the most influential evolutionary patterns in temporal community detection. Firstly, we obtain the temporal community structure based on very successful temporal community detection methods. Secondly, we extract features of nodes based on the structure of the dynamic network, and take the community transition behavior of nodes as the binary classification problem. Finally, we use the decision tree to find the node-level features that have a general impact on node transition. Experiments indicate that the degree and average neighbor degree of nodes have the most common indispensable impact on the node transition behavior, which are very helpful for modeling dynamic complex networks in future.

Introduction

Complex network analysis [1], [2] has received increasing attention from researchers in different fields, including computer science, social science, and physical science [3], [4], [5]. Complex networks always consist of nodes and edges, which represent the objects and the interactions between the objects, respectively. For example, in a social network, nodes could be the social accounts and edges represent the following or followed relationships between accounts. As one of the most important and powerful data structures, analyzing and modeling complex networks can be used for many missions, such as social interaction pattern analysis, social recommendation and protein functional modules recognition. As the most fundamental tasks in complex networks, node identification, link prediction and information dissemination have been widely studied and concerned. In addition, community detection is also one of the most significant tasks, which is usually defined as identifying tightly linked subgraphs from complex networks and benefiting from other tasks.

In general, detecting community structures can help us recognize meaningful modules of a network. A variety of works for community detection have been developed, such as modularity-based methods [6], model-based methods [7], [8] and random walk-based methods [9], [10], [11], where comprehensive surveys can be seen in [12], [13]. However, all these methods assume that the target network is static, that is, the network structure is invariant. Virtually, the network structure varies over time, i.e. dynamic networks. More specifically, in a dynamic network, the nodes may birth or death with time and links between two nodes may appear or disappear. For dynamic network modeling, we usually reply to it as a series of snapshots or slices, each of which can be regarded as a static network. From the perspective of community detection, compared with static networks, detecting the dynamic community poses new challenges [14], among which, how to fuse consecutive snapshot networks to improve performance of community detection and how to describe the evolution of communities are the most important.

Take a co-author network as an example, just as shown in Fig. 1, we show two snapshots of the dynamic network based on the DBLP data [15]. The nodes and edges are the authors and their cooperative relationship, and nodes with the same color represent the same community to which they belong. These three communities are the authors from data mining, database and machine learning, respectively. From the last snapshot to the next, a very important phenomenon is that the research field of some nodes has changed, for example, an author from the database joins into the data mining with the time going by and varying of the network. This is a critical behavior of community detection in dynamic networks, i.e. the transition behavior of nodes, which is the most widely considered dynamic pattern and also is our concern in this paper.

In recent years, more and more attention has been paid to dynamic community detection and different methods have been proposed, including two-step methods, evolutionary clustering methods and model-based methods. Two-step based methods [16], [17] usually apply a static community detection algorithm to each snapshot, and then perform community matching step at adjacent time slices. This kind of methods is not accurate enough because data in the real world is often noisy. Moreover, such a two-step process usually results in unstable community structures and consequentially, unwarranted community evolution [15]. Evolutionary clustering is firstly devoted to clustering the stream data and has been developed for dynamic community detection, the previous or historical network or community information are integrated into the community detection in following subsequent network snapshots, such as the evolutionary spectral clustering, dynamic non-negative matrix factorization and multi-objective evolutionary clustering [18], [19], this type of methods is still the most widely studied and used. The model-based methods [20], [21] usually define a series of network generation mechanisms to reconstruct the dynamic complex network and analyze the evolution of communities, such as the dynamic stochastic block model DSBM [15], which denoted the dynamic pattern based on the classic SBM and transforming community detection and evolution into the parameter estimation. On the whole, the model-based methods have very high computational complexity.

As we all know, all the existing methods for dynamic community detection are focusing on the performance of community detection and the evolutionary patterns or events, while ignoring the internal relevance between the structure varying of dynamic network and the evolution pattern of communities. Therefore, we are interested in, how the structural information of nodes affects the community transitions. In other words, community evolution is usually driven by node transition, and the relationship between the transition behavior and the local varying of nodes is our concern. Although some model-based methods (e.g. [22], [23]) use the degree of nodes to improve the accuracy of community detection, these methods only make the node distribution within a community following the power law and do not reveal the relationship between nodes degree and community evolution. As we have discussed, what kind of nodes are more likely to transfer their communities? Are there more statistical features related to the transfer behavior of nodes? Which is the most important feature? We believe that this could help us design more suitable models for community discovery in dynamic networks.

Our motivation is to explore which local structure information or features of the node has important impact on the transition behavior of nodes in dynamic networks, and which structural feature has a larger influence and which one has a small impact. So in this paper, for a given dynamic network, we firstly obtain its community structure based on three very successful temporal community detection methods. Then, we extract the ten features of nodes based on the structure of the previous snapshot network, and take the community transition behavior of nodes as the binary classification problem. In detail, we use the decision tree as the classification model to find the node-level features that have a general impact on node transition and analyze the community evolution on all the snapshots of the dynamic network. We take the framework on $15$ real-world dynamic networks shows that the degree and average neighbor degree of nodes are the most two important features impacting on the node transition behavior. We believe that this is very helpful for modeling dynamic complex networks in future. The specific contributions of this paper are as follows:

• As far as we know, this paper is the first exploration of the problem that what kind of nodes is more likely to transfer its community, it is the most important behavior in dynamic networks.

• We extract the community features of the nodes belonging and features of the nodes themselves, and treat the node’s community transition as a binary classification problem, then use these features to classify whether the nodes are transferred or not.

• We find that the important common feature of the node’s community transition is node’s average neighbor degree and node’s degree. And node’s average neighbor degree is even more important than node’s degree, which is inconsistent with our previous understanding.