The Many Faces of Graph Dynamics

The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is known today about the network dynamics: indeed, complex networks in reality are not static, but rather dynamically evolve over time. Our paper is motivated by the empirical observation that network evolution patterns seem far from random, but exhibit structure. Moreover, the specific patterns appear to depend on the network type, contradicting the existence of a one fits it all model. However, we still lack observables to quantify these intuitions, as well as metrics to compare graph evolutions. Such observables and metrics are needed for extrapolating or predicting evolutions, as well as for interpolating graph evolutions. To explore the many faces of graph dynamics and to quantify temporal changes, this paper suggests to build upon the concept of centrality, a measure of node importance in a network. In particular, we introduce the notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type. Intuitively, centrality distances reflect the extent to which (non-anonymous) node roles are different or, in case of dynamic graphs, have changed over time, between two graphs. We evaluate the centrality distance approach for five evolutionary models and seven real-world social and physical networks. Our results empirically show the usefulness of centrality distances for characterizing graph dynamics compared to a null-model of random evolution, and highlight the differences between the considered scenarios. Interestingly, our approach allows us to compare the dynamics of very different networks, in terms of scale and evolution speed.

Request Complexity of VNet Topology Extraction: Dictionary-Based Attacks

The network virtualization paradigm envisions an Internet where arbitrary virtual networks (VNets) can be specified and embedded over a shared substrate (e.g., the physical infrastructure). As VNets can be requested at short notice and for a desired time period only, the paradigm enables a flexible service deployment and an efficient resource utilization. This paper investigates the security implications of such an architecture. We consider a simple model where an attacker seeks to extract secret information about the substrate topology, by issuing repeated VNet embedding requests. We present a general framework that exploits basic properties of the VNet embedding relation to infer the entire topology. Our framework is based on a graph motif dictionary applicable for various graph classes. Moreover, we provide upper bounds on the request complexity, the number of requests needed by the attacker to succeed.