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

Understanding Stability of Noisy Networks through Centrality Measures and Local Connections