Geometry of network security

The main point of this paper is that network security has a geometric component, in the sense that some architectures promote some aspects of security. Such security issues closely related to the topological architecture of the network graph are multi-path routing to mitigate "eavesdropping" or "packet sniffing", worm propagation and defense, and distributed denial of service (DDoS) attack mitigation. Those geometric aspects relevant to network security are encapsulated in the concept of graph curvature. An architecture that promotes, in some sense, security is the negative curvature of the graph, which is shown to hold in several physical and logical graphs and in the well know "scale free" model.