Some of the main known results about efficiency, vulnerability and cost for complex networks
are reviewed from a mathematical perspective. Such presentation is then completed by …

The rupture degree of a graph is a measure of the vulnerability of a graph. In this paper we
investigate a refinement that involves the weak version of the parameter. The weak-rupture …

The concept of weak hub-integrity is introduced as a new measure of the stability of a graph
G and it is defined as WHI (G)= min {| S|+ me (GS)}, where S is a hub set and me (GS) …

With the growing demand for information transport, networks and network architecture have
grown increasingly vital. Nodes and the connections that connect them make up a …

The problem of analysis of the vulnerability of single-commodity and multi-commodity
networks taking into account complete breakdown of one or several arcs is considered. The …

Рассмотрена проблема анализа уязвимости однопродуктовой и многопродуктовой
сетей с учетом выхода из строя полностью одного или нескольких ребер. Критерием …

In a communication network, several vulnerability measures are used to determine the
resistance of the network to disruption of operation after the failure of certain stations or …

Connectivity has been used in the past to describe the stability of graphs. If two graphs, have
the same connectivity, then it dose not distinguish between these graphs. That is, the …