Many systems of interacting elements can be conceptualized as networks, where network nodes represent the elements and network ties represent interactions between the elements. In systems where the underlying network evolves, it is useful to determine the points in time where the network structure changes significantly as these may correspond to functional change points. We propose a method for detecting change points in correlation networks that, unlike previous change point detection methods designed for time series data, requires minimal distributional assumptions. We investigate the difficulty of change point detection near the boundaries of the time series in correlation networks and study the power of our method and competing methods through simulation. We also show the generalizable nature of the method by applying it to stock price data as well as fMRI data. Many systems of scientific and societal interest are composed of a large number of interacting elements, examples ranging from proteins interacting within each living cell to people interacting with one another within and across societies. These and many other systems can be conceptualized as networks, where network nodes represent the elements in a given system and network ties represent interactions between the elements. Network science and network analysis are used to analyze and model the structure of interactions in a network, an approach that is commonly motivated by the premise that network structure is associated with the dynamical behavior exhibited by the network, which in turn is expected to be associated with its function. In many cases, however, network structure is not static but instead evolves in time. This suggests that given a sequence of networks, it would be useful to determine points in time where the structure of the network changes in a non-trivial manner. Determining these points is known as the network change point detection problem. Given the connection between network structure and function, it seems reasonable to conjecture that a change in network structure may be coupled with a change in network function. Consequently, detecting structural change points for networks could be informative about functional change points as well. In this paper, we consider the change point detection problem for correlation networks. These networks belong to a class of networks sometimes called similarity networks and they are obtained by defining the edges based on some form of similarity or correlation measure between each pair of nodes 1 . Examples of correlation networks appear in many financial and biological contexts, such as stock market price and gene expression data 2-6 . In general, when evaluating correlation networks, the full data is used to estimate the correlations between the nodes. When using this approach for longitudinal data, it is sometimes implied that the network structure is the same over time. This assumption may however be inaccurate in some cases. For example, in Onnela et al. 2 a stock market correlation network is created from almost two decades of stock prices. In reality the relationship between the stocks, and therefore the structure of the underlying network, likely change over such a long period of time, an issue that they addressed by dividing the data into shorter time windows. Similarly, in functional magnetic resonance imaging (fMRI) trials it is likely that the brain interacts differently during different tasks 7 , or possibly even within a given task, so it may be inaccurate to assume a constant brain activity correlation network in trials with multiple tasks. Suppose that a network is constant or may be assumed so until a known point in time before undergoing sudden change. The alternative, where network change occurs gradually, is not considered here. In the case of sudden change, the underlying data should be split up at the change point into two parts, and two separate correlation networks should be constructed from the two subsets of the data. In reality the location of the change point, or possibly several change points, is not known a priori and must also be inferred from the data. This problem belongs to a wider class of so-called change point detection problems, which has been studied in the field of process control. When the observed node characteristics are independent and normally distributed, methods exist for general time series data to detect changes in the multivariate normal mean or covariance [8] [9] [10] . Dropping the normality assumption, there are also univariate 11-13 and multivariate 11, 14, 15 change point detection methods for shifts in the
Among the already published works in detecting changes in stationarity, we mention Barnett et al. REF , whose paper deals with the problem of monitoring correlation networks by means of a change point method.
Change Point Detection in Correlation Networks