In this paper, we develop a novel Backtrackless Aligned-Spatial Graph Convolutional Network (BASGCN) model to learn effective features for graph classification. Our idea is to transform arbitrary-sized graphs into fixed-sized backtrackless aligned grid structures and define a new spatial graph convolution operation associated with the grid structures. We show that the proposed BASGCN model not only reduces the problems of information loss and imprecise information representation arising in existing spatially-based Graph Convolutional Network (GCN) models, but also bridges the theoretical gap between traditional Convolutional Neural Network (CNN) models and spatially-based GCN models. Furthermore, the proposed BASGCN model can both adaptively discriminate the importance between specified vertices during the convolution process and reduce the notorious tottering problem of existing spatially-based GCNs related to the Weisfeiler-Lehman algorithm, explaining the effectiveness of the proposed model. Experiments on standard graph datasets demonstrate the effectiveness of the proposed model.

The von Neumann entropy of a graph is a spectral complexity measure that has recently found applications in complex networks analysis and pattern recognition. Two variants of the von Neumann entropy exist based on the graph Laplacian and normalized graph Laplacian, respectively. Due to its computational complexity, previous works have proposed to approximate the von Neumann entropy, effectively reducing it to the computation of simple node degree statistics. Unfortunately, a number of issues surrounding the von Neumann entropy remain unsolved to date, including the interpretation of this spectral measure in terms of structural patterns, understanding the relation between its two variants and evaluating the quality of the corresponding approximations. In this article, we aim to answer these questions by first analysing and comparing the quadratic approximations of the two variants and then performing an extensive set of experiments on both synthetic and real-world graphs. We find that (1) the two entropies lead to the emergence of similar structures, but with some significant differences; (2) the correlation between them ranges from weakly positive to strongly negative, depending on the topology of the underlying graph; (3) the quadratic approximations fail to capture the presence of non-trivial structural patterns that seem to influence the value of the exact entropies; and (4) the quality of the approximations, as well as which variant of the von Neumann entropy is better approximated, depends on the topology of the underlying graph.

One of the greatest concerns related to the popularity of GPS-enabled devices and applications is the increasing availability of the personal location information generated by them and shared with application and service providers. Moreover, people tend to have regular routines and be characterized by a set of “significant places”, thus making it possible to identify a user from his/her mobility data. In this paper we present a series of techniques for identifying individuals from their GPS movements. More specifically, we study the uniqueness of GPS information for three popular datasets, and we provide a detailed analysis of the discriminatory power of speed, direction and distance of travel. Most importantly, we present a simple yet effective technique for the identification of users from location information that are not included in the original dataset used for training, thus raising important privacy concerns for the management of location datasets.

In this paper we propose a quantum algorithm to measure the similarity between a pair of unattributed graphs. We design an experiment where the two graphs are merged by establishing a complete set of connections between their nodes and the resulting structure is probed through the evolution of continuous-time quantum walks. In order to analyze the behavior of the walks without causing wave function collapse, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the divergence between the evolution of two suitably initialized quantum walks over this structure is maximum when the original pair of graphs is isomorphic. We also prove that under special conditions the divergence is minimum when the sets of eigenvalues of the Hamiltonians associated with the two original graphs have an empty intersection.