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...

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>

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...

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...