To find interesting structure in networks, community detection algorithms have to take into account not only the network topology, but also dynamics of interactions between nodes. We investigate this claim using the paradigm of synchronization in a network of coupled oscillators. As the network evolves to a global steady state, nodes belonging to the same community synchronize faster than nodes belonging to different communities. Traditionally, nodes in network synchronization models are coupled via one-to-one, or conservative interactions. However, social interactions are often one-to-many, as for example, in social media, where users broadcast messages to all their followers. We formulate a novel model of synchronization in a network of coupled oscillators in which the oscillators are coupled via one-to-many, or non-conservative interactions. We study the dynamics of different interaction models and contrast their spectral properties. To find multi-scale community structure in a network of interacting nodes, we define a similarity function that measures the degree to which nodes are synchronized and use it to hierarchically cluster nodes. We study real-world social networks, including networks of two social media providers. To evaluate the quality of the discovered communities in a social media network we propose a community quality metric based on user activity. We find that conservative and non-conservative interaction models lead to dramatically different views of community structure even within the same network. Our work offers a novel mathematical framework for exploring the relationship between network structure, topology and dynamics.
It might be argued that taking interactions into account eventually leads to a weighted graph and off-the shelf community detection algorithms for weighted graphs @cite_4 might be applied. However, like in the unweighted case, application of a community detection method on a weighted graph without taking the nature of interaction process into account, might lead to unsatisfactory results. For example, if conductance minimization algorithm is applied on a weighted graph, whose weights are a consequence of a non-conservative process, the structure detected might differ significantly from ground truth. Our method on the other hand learns the weights from the interaction process and then detects structure dynamically. Learning the underlying interaction process from the activity logs of nodes of the network and using this process to determine the community structure is the course of future work.
@cite_4
2127048411
Community detection is a common problem in various types of big graphs. It is meaningful to understand the functions and dynamics of networks. The challenges of detecting community for big graphs include high computational cost, no prior information, etc.. In this work, we analyze the process of random walking in graphs, and find out that the weight of an edge gotten by processing the vertices visited by the walker could be an indicator to measure the closeness of vertex connection. Based on this idea, we propose a community detection algorithm for undirected big graphs which consists of three steps, including random walking using a single walker, weight calculating for edges and community detecting. Our algorithm is running in O(n2) without prior information. Experimental results show that our algorithm is capable of detecting the community structure and the overlapping parts of graphs in real-world effectively, and handling the challenges of community detection in big graph era.