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 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 a neuron position alignment method 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, a cross-correlation based method and a causal Bayesian network method are 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 its topology.