Graph Distance Measures based on Intragraph Clustering and Cluster Distance

Abstract

Various graph distance measures were considered in previous chapters. All of these measures have in common that the distance of two given graphs g1 and g2 is equal to zero if and only if g1 and g2 are isomorphic to each other. Sometimes, however, it may be desirable to have a more flexible distance measure for which d(g1, g2) = 0 if g1 and g2 are similar, but not necessarily isomorphic. Such a measure is potentially useful to make our graph-distance-based computer network monitoring procedures more robust against noise and small random perturbations.