  In the correlation clustering problem for complete signed graphs, the input
is a complete signed graph with edges weighted as $+1$ (denote recommendation
to put this pair in the same cluster) or $-1$ (recommending to put this pair of
vertices in separate clusters) and the target is to cluster the set of vertices
such that the number of disagreements with these recommendations is minimized.
  In this paper, we consider the problem of correlation clustering for dynamic
complete signed graphs where (1) a vertex can be added or deleted, and (2) the
sign of an edge can be flipped. In the proposed online scheme, the offline
approximation algorithm in [CALM+21] for correlation clustering is used. Up to
the author's knowledge, this is the first online algorithm for dynamic graphs
which allows a full set of graph editing operations.
  The proposed approach is rigorously analyzed and compared with a baseline
method, which runs the original offline algorithm on each time step. Our
results show that the dynamic operations have local effects on the neighboring
vertices and we employ this locality to reduce the dependency of the running
time in the Baseline to the summation of the degree of all vertices in $G_t$,
the graph after applying the graph edit operation at time step $t$, to the
summation of the degree of the changing vertices (e.g. two endpoints of an
edge) and the number of clusters in the previous time step. Moreover, the
required working memory is reduced to the square of the summation of the degree
of the modified edge endpoints rather than the total number of vertices in the
graph.
