Modern brain mapping techniques are producing increasingly large datasets of anatomical or functional connection patterns. Recently, it became possible to record detailed live imaging videos of mammal brain while the subject is engaging routine activity. We analyze a dataset of videos recorded from ten mice to describe how to detect neurons, extract neuron signals, map correlation of neuron signals to mice activity, detect the network topology of active neurons, and analyze network topology characteristics. We propose neuron position alignment to compensate the distortion and movement of cerebral cortex in live mouse brain and the background luminance compensation to extract and model neuron activity. To find out the network topology as an undirected graph model, a cross-correlation based method is proposed and used for analysis. Afterwards, we did preliminary analysis on network topologies. The significance of this paper is on how to extract neuron activities from live mouse brain imaging videos and a network analysis method to analyze topology that can potentially provide insight on how neurons are actively connected under stimulus, rather than analyzing static neural networks.