Physiological Brain connectivity and spontaneous interaction between regions of interest of the brain can be represented by a matrix (full or sparse) or equivalently by a complex network called connectome. This representation of brain connectivity is adopted when comparing different patterns of structural and functional connectivity to null models or between groups of individuals. Two levels of comparison could be considered when analyzing brain connectivity: the global level and the local level. In the global level, the whole brain information is summarized by one summary statistic, whereas in the local analysis, each region of interest of the brain is summarized by a specific statistic. We show that these levels are mutually informatively integrative in some extent. We present different methods of analysis at both levels, the most relevant global and local network measures. We discuss as well the assumptions to be satisfied for each method; the error rates controlled by each method, and the challenges to overcome, especially, in the local case. We also highlight the possible factors that could influence the statistical results and the questions that have to be addressed in such analyses.