Topic

# Adjacency list

About: Adjacency list is a(n) research topic. Over the lifetime, 4419 publication(s) have been published within this topic receiving 78449 citation(s).

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TL;DR: A general framework for `soft' thresholding that assigns a connection weight to each gene pair is described and several node connectivity measures are introduced and provided empirical evidence that they can be important for predicting the biological significance of a gene.

Abstract: Gene co-expression networks are increasingly used to explore the system-level functionality of genes. The network construction is conceptually straightforward: nodes represent genes and nodes are connected if the corresponding genes are significantly co-expressed across appropriately chosen tissue samples. In reality, it is tricky to define the connections between the nodes in such networks. An important question is whether it is biologically meaningful to encode gene co-expression using binary information (connected=1, unconnected=0). We describe a general framework for ;soft' thresholding that assigns a connection weight to each gene pair. This leads us to define the notion of a weighted gene co-expression network. For soft thresholding we propose several adjacency functions that convert the co-expression measure to a connection weight. For determining the parameters of the adjacency function, we propose a biologically motivated criterion (referred to as the scale-free topology criterion). We generalize the following important network concepts to the case of weighted networks. First, we introduce several node connectivity measures and provide empirical evidence that they can be important for predicting the biological significance of a gene. Second, we provide theoretical and empirical evidence that the ;weighted' topological overlap measure (used to define gene modules) leads to more cohesive modules than its ;unweighted' counterpart. Third, we generalize the clustering coefficient to weighted networks. Unlike the unweighted clustering coefficient, the weighted clustering coefficient is not inversely related to the connectivity. We provide a model that shows how an inverse relationship between clustering coefficient and connectivity arises from hard thresholding. We apply our methods to simulated data, a cancer microarray data set, and a yeast microarray data set.

3,573 citations

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TL;DR: A novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated, resulting in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree and is able to handle very large graphs with several hundred thousand vertices.

Abstract: A novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated. The data to be clustered are represented by an undirected adjacency graph G with arc capacities assigned to reflect the similarity between the linked vertices. Clustering is achieved by removing arcs of G to form mutually exclusive subgraphs such that the largest inter-subgraph maximum flow is minimized. For graphs of moderate size ( approximately 2000 vertices), the optimal solution is obtained through partitioning a flow and cut equivalent tree of G, which can be efficiently constructed using the Gomory-Hu algorithm (1961). However for larger graphs this approach is impractical. New theorems for subgraph condensation are derived and are then used to develop a fast algorithm which hierarchically constructs and partitions a partially equivalent tree of much reduced size. This algorithm results in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree and is able to handle very large graphs with several hundred thousand vertices. The new clustering algorithm is applied to the image segmentation problem. The segmentation is achieved by effectively searching for closed contours of edge elements (equivalent to minimum cuts in G), which consist mostly of strong edges, while rejecting contours containing isolated strong edges. This method is able to accurately locate region boundaries and at the same time guarantees the formation of closed edge contours. >

1,175 citations

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Osaka University

^{1}TL;DR: A novel approach named AGM to efficiently mine the association rules among the frequently appearing substructures in a given graph data set through the extended algorithm of the basket analysis is proposed.

Abstract: This paper proposes a novel approach named AGM to efficiently mine the association rules among the frequently appearing substructures in a given graph data set A graph transaction is represented by an adjacency matrix, and the frequent patterns appearing in the matrices are mined through the extended algorithm of the basket analysis Its performance has been evaluated for the artificial simulation data and the carcinogenesis data of Oxford University and NTP Its high efficiency has been confirmed for the size of a real-world problem

1,089 citations

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TL;DR: This paper presents a new method for visualizing compound graphs based on visually bundling the adjacency edges, i.e., non-hierarchical edges, together and discusses the results based on an informal evaluation provided by potential users of such visualizations.

Abstract: A compound graph is a frequently encountered type of data set. Relations are given between items, and a hierarchy is defined on the items as well. We present a new method for visualizing such compound graphs. Our approach is based on visually bundling the adjacency edges, i.e., non-hierarchical edges, together. We realize this as follows. We assume that the hierarchy is shown via a standard tree visualization method. Next, we bend each adjacency edge, modeled as a B-spline curve, toward the polyline defined by the path via the inclusion edges from one node to another. This hierarchical bundling reduces visual clutter and also visualizes implicit adjacency edges between parent nodes that are the result of explicit adjacency edges between their respective child nodes. Furthermore, hierarchical edge bundling is a generic method which can be used in conjunction with existing tree visualization techniques. We illustrate our technique by providing example visualizations and discuss the results based on an informal evaluation provided by potential users of such visualizations

998 citations

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IBM

^{1}TL;DR: This work presents a simple, effective, and efficient technique for approximating arbitrary polyhedra based on triangulation and vertex-clustering, and produces a series of 3D approximations that resemble the original object from all viewpoints, but contain an increasingly smaller number of faces and vertices.

Abstract: We present a simple, effective, and efficient technique for approximating arbitrary polyhedra. It is based on triangulation and vertex-clustering, and produces a series of 3D approximations (also called “levels of detail”) that resemble the original object from all viewpoints, but contain an increasingly smaller number of faces and vertices. The simplification is more efficient than competing techniques because it does not require building and maintaining a topological adjacency graph. Furthermore, it is better suited for mechanical CAD models which often exhibit patterns of small features, because it automatically groups and simplifies features that are geometrically close, but need not be topologically close or even part of a single connected component Using a lower level of detail when displaying small, distant, or background objects improves graphic performance without a significant loss of perceptual information, and thus enables realtime inspection of complex scenes or a convenient environment for animation or walkthrough preview.

836 citations