Topic
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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TL;DR: With this generalized algorithm it is possible, for a variety of value systems, to calculate the values of the paths and cycles of lengthn in a network and to construct its value matrix of simplen-sequences.
Abstract: An algorithm is presented for constructing from the adjacency matrix of a digraph the matrix of its simplen-sequences. In this matrix, thei, j entry,i ≠j, gives the number of paths of lengthn from a pointv
i
to a pointv
j
; the diagonal entryi, i gives the number of cycles of lengthn containingv
i
. The method is then generalized to networks—that is, digraphs in which some value is assigned to each line. With this generalized algorithm it is possible, for a variety of value systems, to calculate the values of the paths and cycles of lengthn in a network and to construct its value matrix of simplen-sequences. The procedures for obtaining the two algorithms make use of properties of a line digraph—that is, a derived digraph whose points and lines represent the lines and adjacency of lines of the given digraph.
30 citations
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01 Jan 2014TL;DR: It can be concluded that an DSOMA population does behave like a complex network, and therefore can be analysed as such, in order to obtain information about population development.
Abstract: This research analyses the development of a complex network in the swarm based Discrete Self-Organising Migrating Algorithm (DSOMA). The main aim is to evaluate if a complex network is generated in DSOMA, and how the population can be evaluated when the objective is to optimise the flow shop scheduling with blocking problem. The population is evaluated as a complex network over a number of migrations, and different attributes such as adjacency graph, minimal cut, degree centrality, closeness centrality, betweenness centrality, Katz centrality, mean neighbour degree, k-Clique, k-Plan, k-Club, k-Clan and community graph plots are analysed. From the results, it can be concluded that an DSOMA population does behave like a complex network, and therefore can be analysed as such, in order to obtain information about population development.
30 citations
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TL;DR: The main result is generalized for classes in which the assignment of sets to vertices must be one-to-one, as well as for classes of simplicial complexes arising as nerves of sets from a pre-specified family.
30 citations
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TL;DR: The Fibonacci polynomials are studied over GF(2) with particular emphasis on their divisibility properties and their relation to the existence of even dominating sets in grid graphs and properties of a corresponding recurrence.
Abstract: A non-empty set of vertices is called an even dominating set if each vertex in the graph is adjacent to an even number of vertices in the set (adjacency is reflexive). In this paper, the Fibonacci polynomials are studied over GF(2) with particular emphasis on their divisibility properties and their relation to the existence of even dominating sets in grid graphs and properties of a corresponding recurrence.
30 citations
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06 Nov 1994TL;DR: A new partial consistency suited to these problems: the semi-geometric arc-consistency is defined; the method for achieving it is based on an inference by propagation rectangle label and interval label.
Abstract: We describe a knowledge-based system that generates all possible floor plans satisfying a set of geometric constraints on the rooms (non-overlap, adjacency, minimal/maximal area, minimal/maximal dimension, etc.). Our approach is based on the extension of the constraint techniques; we define in particular a new partial consistency suited to these problems: the semi-geometric arc-consistency. The method for achieving it is based on an inference by propagation rectangle label and interval label. After solving some realistic problems, we conclude by discussing the relevance of a constraint-based approach for solving these problems. >
30 citations