For a graph G, we can consider the minimum number of vertices (resp. edges) whose deletion disconnects the graph and such that two of the components created by teh removal of the vertices (resp. the edges, satisfy no additional condition (usual connectivities) or must contain: at least one edge (#connectivities) or at least one cycle (cyclic connectivities). Thus, we can define six sorts of connectivity for a given graph. In this paper, we give upper bounds for the different types of connectivity and results about the graphs reaching these upper bounds or having connectivity 0 and we investigate relations between these six sorts of connectivity.
