  Networks created from real-world data contain some inaccuracies or noise,
manifested as small changes in the network structure. An important question is
whether these small changes can significantly affect the analysis results. In
this paper, we study the effect of noise in changing ranks of the high
centrality vertices. We compare, using the Jaccard Index (JI), how many of the
top-k high centrality nodes from the original network are also part of the
top-k ranked nodes from the noisy network. We deem a network as stable if the
JI value is high. We observe two features that affect the stability. First, the
stability is dependent on the number of top-ranked vertices considered. When
the vertices are ordered according to their centrality values, they group into
clusters. Perturbations to the network can change the relative ranking within
the cluster, but vertices rarely move from one cluster to another. Second, the
stability is dependent on the local connections of the high ranking vertices.
The network is highly stable if the high ranking vertices are connected to each
other. Our findings show that the stability of a network is affected by the
local properties of high centrality vertices, rather than the global properties
of the entire network. Based on these local properties we can identify the
stability of a network, without explicitly applying a noise model.
