2 research outputs found
Homophyly and Randomness Resist Cascading Failure in Networks
The universal properties of power law and small world phenomenon of networks
seem unavoidably obstacles for security of networking systems. Existing models
never give secure networks. We found that the essence of security is the
security against cascading failures of attacks and that nature solves the
security by mechanisms. We proposed a model of networks by the natural
mechanisms of homophyly, randomness and preferential attachment. It was shown
that homophyly creates a community structure, that homophyly and randomness
introduce ordering in the networks, and that homophyly creates inclusiveness
and introduces rules of infections. These principles allow us to provably
guarantee the security of the networks against any attacks. Our results show
that security can be achieved provably by structures, that there is a tradeoff
between the roles of structures and of thresholds in security engineering, and
that power law and small world property are never obstacles for security of
networks
Dimensions, Structures and Security of Networks
One of the main issues in modern network science is the phenomenon of
cascading failures of a small number of attacks. Here we define the dimension
of a network to be the maximal number of functions or features of nodes of the
network. It was shown that there exist linear networks which are provably
secure, where a network is linear, if it has dimension one, that the high
dimensions of networks are the mechanisms of overlapping communities, that
overlapping communities are obstacles for network security, and that there
exists an algorithm to reduce high dimensional networks to low dimensional ones
which simultaneously preserves all the network properties and significantly
amplifies security of networks. Our results explore that dimension is a
fundamental measure of networks, that there exist linear networks which are
provably secure, that high dimensional networks are insecure, and that security
of networks can be amplified by reducing dimensions.Comment: arXiv admin note: text overlap with arXiv:1310.804