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Adjacency list

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


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01 Apr 2004
TL;DR: The notion that proximity or adjacency at different orders might form more appropriate measures of syntax distance is introduced, the proximity of nodes to nodes and lines to lines in the dual and the primal being illustrated for both Gassin and central Melbourne.
Abstract: We explore ways of introducing Euclidean distances associated with street systemsrepresented by axial lines into the two connectivity graphs based on points (or streetjunctions), and on lines (or streets), the so-called dual and primal representations ofthe space syntax problem. As the axial line is embedded in the connectivity graphbetween the points, for the dual problem the specification of Euclidean distancebetween points is relatively trivial but for the original syntax problem, this isproblematic in that it requires us to find a unique point representation for each line.The key is to find the centroids of the lines (of sight or unobstructed movement)between the points on each axial line, and then to use these to form a weightedcentroid of centroids. The distances between axial lines which form paths through theconnectivity graph between streets, are then computed using these centroids asstarting points for each line and routing distance through the street junctions.There are many issues involving interpretation of these measures. It might be thoughtthat the longer an axial line, the more important it is. But by giving an axial linedistance, this suggests that this is a deterrence to interaction, as in spatial interactiontheory, with longer axial lines being individually less important, notwithstanding theprobability that they are better connected within the overall street system. Clearly inmany finer-scale morphologies, this assumption might not be tenable but the measuresdeveloped here can be easily adapted to various circumstances. What this focus ondistance enables us to do is to treat a ?mixed syntax? problem where we are able toembed truly planar graphs into the axial map. This extends the technique to deal withsystems not only comprising streets down which we can see, but also fixed rail lines,subway systems, footpaths and so on which currently are hard to handle in thetraditional theory. We illustrate the extended theory for a pure syntax problem, theFrench village of Gassin, and a mixed syntax problem based on the grid of streets andunderground railways in central Melbourne. In conclusion, we introduce the notionthat proximity or adjacency at different orders might form more appropriate measuresof syntax distance, the proximity of nodes to nodes and lines to lines in the dual andthe primal being illustrated for both Gassin and central Melbourne.

23 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that if a graph G$ has no cycle of length more than four or five vertices, then G$ is cospectral with a graph H$ and H$ is connected and planar.
Abstract: ‎Let $n$ be any positive integer and $F_n$ be the friendship (or Dutch windmill) graph with $2n+1$ vertices and $3n$ edges‎. ‎Here we study graphs with the same adjacency spectrum as $F_n$‎. ‎Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same‎. ‎Let $G$ be a graph cospectral with $F_n$‎. ‎Here we prove that if $G$ has no cycle of length $4$ or $5$‎, ‎then $Gcong F_n$‎. ‎Moreover if $G$ is connected and planar then $Gcong F_n$‎. ‎All but one of connected components of $G$ are isomorphic to $K_2$‎. ‎The complement $overline{F_n}$ of the friendship graph is determined by its adjacency eigenvalues‎, ‎that is‎, ‎if $overline{F_n}$ is cospectral with a graph $H$‎, ‎then $Hcong overline{F_n}$‎.

23 citations

Proceedings ArticleDOI
12 Oct 2020
TL;DR: This work designs a simple and highly modularized graph convolutional network architecture for skeleton-based action recognition by repeating a building block that aggregates multi-granularity information from both the spatial and temporal paths.
Abstract: Skeleton-based human action recognition has attracted much attention with the prevalence of accessible depth sensors. Recently, graph convolutional networks (GCNs) have been widely used for this task due to their powerful capability to model graph data. The topology of the adjacency graph is a key factor for modeling the correlations of the input skeletons. Thus, previous methods mainly focus on the design/learning of the graph topology. But once the topology is learned, only a single-scale feature and one transformation exist in each layer of the networks. Many insights, such as multi-scale information and multiple sets of transformations, that have been proven to be very effective in convolutional neural networks (CNNs), have not been investigated in GCNs. The reason is that, due to the gap between graph-structured skeleton data and conventional image/video data, it is very challenging to embed these insights into GCNs. To overcome this gap, we reinvent the split-transform-merge strategy in GCNs for skeleton sequence processing. Specifically, we design a simple and highly modularized graph convolutional network architecture for skeleton-based action recognition. Our network is constructed by repeating a building block that aggregates multi-granularity information from both the spatial and temporal paths. Extensive experiments demonstrate that our network outperforms state-of-the-art methods by a significant margin with only 1/5 of the parameters and 1/10 of the FLOPs.

23 citations

Journal ArticleDOI
TL;DR: A feature oriented and knowledge based generative type CAPP system is presented in the paper and an axiomatic approach is utilized to include the tolerance and machine's precision information in determining the cutting conditions.

23 citations

Journal ArticleDOI
TL;DR: These new algorithms are local, being applicable to a specified 0D cell and the 1D cells described by specified polynomials, and particularly efficient algorithms are given for the 0D cells in spaces of dimensions two, three and four.

22 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023209
2022439
2021283
2020280
2019296
2018232