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Neurons in our brains are responsible for transmitting signals and information through out the brain. They are excitable cells, which can receive both electrical and chemical stimulus and forward these signals to other neurons. Some medical scientists (Power et al., Menon, 2011; Zhou et al., 2011) utilized specific equipment, such as Functional magnetic resonance imaging (fMRI) (Thomas, 1993), to record the behaviors of neurons. However, fMRI requires several seconds of scanning to get an image, which makes it impossible to measure the live real-time simultaneous brain activities on the neuron level. Recent progresses in neural science using calcium imaging were used for microscopic whole-brain imaging (Yuste & Church, 2014). It can record several frames per second on the live brain activities, and thus make it possible for researchers to study collective brain neuron activities towards specific stimulus, e.g., measuring responsive neuron networks in the visual processing area while a mouse is seeing different patterns.
In a sequence of calcium-imaging videos that records live mouse brain neuron activities, each neuron varies between two states: lighting (active mode) and shading (inactive mode). The original image frame in the recorded video is shown in the left of Figure 1. Given the live brain videos, The authors propose a neuron signal extraction method that includes neuron position alignment, background luminance compensation, neuron detection and neuron activity analysis to collect the so-called flashing pattern (active or inactive sequence) of each neuron, as the circles shown in the right of Figure 1. By applying our algorithms to the records, the authors can discover whether the neurons are active in each frame. Without loss of generality, the authors can assume all the neurons are initially inactive before the first stimulus comes. When an inactive neuron was stimulated, it becomes active for a while and then passes this stimulation to other neurons. Afterward, the neuron becomes inactive again. The described flashing patterns of neurons were collected in the video sequences and various conclusions were summarized from observation of video sequences (Power et al., 2011; Zhou et al., 2012). There are some common agreements about the flashing patterns of neurons that can be applied in the related researches:
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First, the duration of active mode or inactive mode for each neuron is independent from others unless they are connected.
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Second, groups of neurons may work together for a certain purpose of brain (Functional Segregation in (Rubinov & Sporns, 2010)). For example, when a person is seeing or thinking, some specific neurons are stimulated by the signal of “seeing” or “thinking” and a bunch of other neurons are triggered to work together.
In order to construct a specific network topology of brain neurons from a given flashing patterns of neurons, firstly, the authors can model the network as a set of neurons V, where 
is the ith neuron with 
and 
is the number of neurons inside this set, in conjunction with a set of edges E between neuron pairs where 
represents the edge between ith and jth neurons, where 
and 
defines the weight of edge between node i and j. Therefore, the connectivities between all neuron pairs inside the brain form a specific network topology which can be described as a graph. By observing the flashing patterns of neurons, the authors propose a network model to analyze interaction between brain neurons. To find out the network topology as an undirected graph model, a cross-correlation based method is proposed and multiple thresholds are chosen to adjust the model. Considering the causality of the brain neuron network, a score-based algorithm is implemented to learn the structure of neuron network as a causal Bayesian network. With network analysis, one of our goals is to find out the key neurons with Small World properties, another goal is to analyze the clustering of brain neurons to understand the functional segregation proposed by (Rubinov & Sporns, 2010).