Topic
Adjacency list
About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.
Papers published on a yearly basis
Papers
More filters
Posted Content•
TL;DR: This study proposes to learn the represention of a graph, or the topological structure of a network, through a deep learning model that significantly improves the effectiveness of existing methods, including linear or nonlinear regressors that use hand-crafted features, graph kernels, and competing deep learning methods.
Abstract: The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted structural features. These representations either fail to highlight local and global properties of the graph or suffer from a severe loss of structural information. There lacks an effective graph representation, which hinges the realization of the predictive power of network structures.
In this study, we propose to learn the represention of a graph, or the topological structure of a network, through a deep learning model. This end-to-end prediction model, named DeepGraph, takes the input of the raw adjacency matrix of a real-world network and outputs a prediction of the growth of the network. The adjacency matrix is first represented using a graph descriptor based on the heat kernel signature, which is then passed through a multi-column, multi-resolution convolutional neural network. Extensive experiments on five large collections of real-world networks demonstrate that the proposed prediction model significantly improves the effectiveness of existing methods, including linear or nonlinear regressors that use hand-crafted features, graph kernels, and competing deep learning methods.
21 citations
Posted Content•
TL;DR: A new data structure, Parallel Adjacency Lists (PAL), for efficiently managing graphs with billions of edges on disk, which can store graphs more compactly while allowing fast access to both the incoming and the outgoing edges of a vertex, without duplicating data.
Abstract: We propose a new data structure, Parallel Adjacency Lists (PAL), for efficiently managing graphs with billions of edges on disk. The PAL structure is based on the graph storage model of GraphChi (Kyrola et. al., OSDI 2012), but we extend it to enable online database features such as queries and fast insertions. In addition, we extend the model with edge and vertex attributes. Compared to previous data structures, PAL can store graphs more compactly while allowing fast access to both the incoming and the outgoing edges of a vertex, without duplicating data. Based on PAL, we design a graph database management system, GraphChi-DB, which can also execute powerful analytical graph computation.
We evaluate our design experimentally and demonstrate that GraphChi-DB achieves state-of-the-art performance on graphs that are much larger than the available memory. GraphChi-DB enables anyone with just a laptop or a PC to work with extremely large graphs.
21 citations
30 Apr 1974
TL;DR: This paper investigates three matrix representations of graphs; the (vertex) adjacency matrix, the edge-adjacency Matrix, and the incidence matrix, which determine an unlabelled graph up to isomorphism.
Abstract: An open problem, posed by A. Rosenberg [R], motivates the consideration of representations of graphs and the effect of these representations on the efficiency of algorithms which determine properties of unlabelled graphs. In this paper we investigate three matrix representations of graphs; the (vertex) adjacency matrix, the edge-adjacency matrix, and the incidence matrix. With the exception of one instance of the edge-adjacency matrix, these structures determine an unlabelled graph up to isomorphism and are, as a result, natural candidates for computer representations of graphs.
21 citations
TL;DR: A cycle of C of a graph G is called a D"@l-cycle if every component of G - V(C) has order less than l, and a path is defined analogously as discussed by the authors.
21 citations
01 Jan 1996
TL;DR: A morphological operator is called connected if it does not split components of the levelsets, but acts on the level of flat zones, and a simple description of such operators can be obtained by representing an image as a region adjacency graph, a graph whose vertices represent the component of the level sets and whose edges describe adjacencies.
Abstract: A morphological operator is called connected if it does not split components of the levelsets, but acts on the level of flat zones. A simple description of such operators can be obtained byrepresenting an image as a region adjacency graph, a graph whose vertices represent the componentsof the level sets and whose edges describe adjacency. In this graph connected operators can onlychange grey-values of the vertices. To obtain the adjacency graph of the transformed image, onehas to merge adjacent vertices which carry the same grey-value.
21 citations