This work focuses on connectivity in a dynamic graph. An undirected graph is defined on a finite and discrete time interval. Edges can appear and disappear over time. The first objective of this work is to extend the notion of connected component to dynamic graphs in a new way. Persistent connected components are defined by their size, corresponding to the number of vertices, and their length, corresponding to the number of consecutive time steps they are present on. The second objective of this work is to develop an algorithm computing the largest, in terms of size and length, persistent connected components in a dynamic graph. PICCNIC algorithm (PersIstent Connected CompoNent InCremental Algorithm) is a polynomial time algorithm of minimal complexity. Another advantage of this algorithm is that it works online: knowing the evolution of the dynamic graph is not necessary to execute it. PICCNIC algorithm is implemented using the GraphStream library and experimented in order to carefully study the outcome of the algorithm according to different input graph types, as well as real data networks, to verify the theoretical complexity, and to confirm its feasibility for graphs of large size.