Adjacency list

About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.

Anonymizing Social Graphs via Uncertainty Semantics

Abstract: Rather than anonymizing social graphs by generalizing them to super nodes/edges or adding/removing nodes and edges to satisfy given privacy parameters, recent methods exploit the semantics of uncertain graphs to achieve privacy protection of participating entities and their relationships. These techniques anonymize a deterministic graph by converting it into an uncertain form. In this paper, we propose a general obfuscation model based on uncertain adjacency matrices that keep expected node degrees equal to those in the unanonymized graph. We analyze two recently proposed schemes and their fitting into the model. We also point out disadvantages in each method and present several elegant techniques to fill the gap between them. Finally, to support fair comparisons, we develop a new tradeoff quantifying framework by leveraging the concept of incorrectness. Experiments on large social graphs demonstrate the effectiveness of our schemes.

Unboundedness of adjacency matrices of locally finite graphs

Abstract: Given a locally finite simple graph so that its degree is not bounded, every self-adjoint realization of the adjacency matrix is unbounded from above. In this note we give an optimal condition to ensure it is also unbounded from below. We also consider the case of weighted graphs. We discuss the question of self-adjoint extensions and prove an optimal criterium.

Learning Grid Cells as Vector Representation of Self-Position Coupled with Matrix Representation of Self-Motion

Abstract: This paper proposes a representational model for grid cells. In this model, the 2D self-position of the agent is represented by a high-dimensional vector, and the 2D self-motion or displacement of the agent is represented by a matrix that transforms the vector. Each component of the vector is a unit or a cell. The model consists of the following three sub-models. (1) Vector-matrix multiplication. The movement from the current position to the next position is modeled by matrix-vector multiplication, i.e., the vector of the next position is obtained by multiplying the matrix of the motion to the vector of the current position. (2) Magnified local isometry. The angle between two nearby vectors equals the Euclidean distance between the two corresponding positions multiplied by a magnifying factor. (3) Global adjacency kernel. The inner product between two vectors measures the adjacency between the two corresponding positions, which is defined by a kernel function of the Euclidean distance between the two positions. Our representational model has explicit algebra and geometry. It can learn hexagon patterns of grid cells, and it is capable of error correction, path integral and path planning.

Fusion Graphs: Merging Properties and Watersheds

Abstract: Region merging methods consist of improving an initial segmentation by merging some pairs of neighboring regions. In this paper, we consider a segmentation as a set of connected regions, separated by a frontier. If the frontier set cannot be reduced without merging some regions then we call it a cleft, or binary watershed. In a general graph framework, merging two regions is not straightforward. We define four classes of graphs for which we prove, thanks to the notion of cleft, that some of the difficulties for defining merging procedures are avoided. Our main result is that one of these classes is the class of graphs in which any cleft is thin. None of the usual adjacency relations on ?2 and ?3 allows a satisfying definition of merging. We introduce the perfect fusion grid on ? n , a regular graph in which merging two neighboring regions can always be performed by removing from the frontier set all the points adjacent to both regions.