We consider a clique relaxation model based on the concept of relative vertex connectivity. It extends the classical definition of a k-vertex-connected subgraph by requiring that the minimum number of vertices whose removal results in a disconnected (or a trivial) graph is proportional to the...

This paper defines and analyzes a generalization of the classical minimum vertex cover problem to the case of two-layer interdependent networks with cascading node failures that can be caused by two common types of interdependence. Previous studies on interdependent networks mainly addressed the...

This paper analytically characterizes certain classes of low-diameter strongly attack-tolerant networks of arbitrary size, which are globally optimal in the sense that they contain the minimum possible number of edges. Strong attack tolerance property of level <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$R$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>R</mi> </math> </EquationSource> </InlineEquation> implies that a...</equationsource></equationsource></inlineequation>

Network robustness issues are crucial in a variety of application areas. In many situations, one of the key robustness requirements is the connectivity between each pair of nodes through a path that is short enough, which makes a network cluster more robust with respect to potential network...