text: Link streams model interactions over time in a wide range of fields. Under this model, the challenge is to mine efficiently both temporal and topological structures. Community detection and change point detection are one of the most powerful tools to analyze such evolving interactions. In this paper, we build on both to detect stable community structures by identifying change points within meaningful communities. Unlike existing dynamic community detection algorithms, the proposed method is able to discover stable communities efficiently at multiple temporal scales. We test the effectiveness of our method on synthetic networks, and on high-resolution time-varying networks of contacts drawn from real social networks.
  @cite_16: Many time-evolving systems in nature, society and technology leave traces of the interactions within them. These interactions form temporal networks that reflect the states of the systems. In this work, we pursue a coarse-grained description of these systems by proposing a method to assign discrete states to the systems and inferring the sequence of such states from the data. Such states could, for example, correspond to a mental state (as inferred from neuroimaging data) or the operational state of an organization (as inferred by interpersonal communication). Our method combines a graph distance measure and hierarchical clustering. Using several empirical data sets of social temporal networks, we show that our method is capable of inferring the system’s states such as distinct activities in a school and a weekday state as opposed to a weekend state. We expect the methods to be equally useful in other settings such as temporally varying protein interactions, ecological interspecific interactions, functional connectivity in the brain and adaptive social networks.
  @cite_4: Interactions among people or objects are often dynamic in nature and can be represented as a sequence of networks, each providing a snapshot of the interactions over a brief period of time. An important task in analyzing such evolving networks is change-point detection, in which we both identify the times at which the large-scale pattern of interactions changes fundamentally and quantify how large and what kind of change occurred. Here, we formalize for the first time the network change-point detection problem within an online probabilistic learning framework and introduce a method that can reliably solve it. This method combines a generalized hierarchical random graph model with a Bayesian hypothesis test to quantitatively determine if, when, and precisely how a change point has occurred. We analyze the detectability of our method using synthetic data with known change points of different types and magnitudes, and show that this method is more accurate than several previously used alternatives. Applied to two high-resolution evolving social networks, this method identifies a sequence of change points that align with known external "shocks" to these networks.
  @cite_17: 
summary: Our work is also related to research conducted on change point detection considering community structures. In these approaches, given a sequence of snapshots, one wants to detect the periods during which the network organization and or the community structure remains stable. In @cite_4 , the authors proposed the first change-point detection method for evolving networks that uses generative network models and statistical hypothesis testing. @cite_17 proposed a hierarchical change point detection method to detect both inter-community(local change) and intra-community(global change) evolution. A recent work by @cite_16 used graph distance measures and hierarchical clustering to identify sequences of system state dynamics. From those methods, our proposal keeps the principle of stable periods delimited by change points, and the idea of detecting changes at local and global scales. But our method differs in two directions: @math we are searching for stable individual communities instead of stable graph periods, and @math we search for stable structures at multiple levels of temporal granularity.