Reflexive relation

Relations

Published in Rowan Garnier, John Taylor, Discrete Mathematics, 2020

We now consider how we can recognize whether a relation satisfies any of these properties given its directed graph or its binary matrix. Firstly, if R is a reflexive relation on a finite set A then a R a for every a ∈ A. This means that, in the directed graph of R, there is a directed arrow from every point to itself. The directed graph of the relation in example 4.1.2 (figure 4.4) has this property. In the binary matrix of a reflexive relation R, there is a one in every position along the diagonal which runs from the top left to the bottom right of the matrix. (This diagonal is called the ‘leading diagonal' of the matrix.)

The impact of node arrival process and stochastic edge growth on scale-free distribution in complex networks

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Journal Information

Published in International Journal of Modelling and Simulation, 2020

F. Safaei, H. Yeganloo, M. Moudi

We start with a formal definition of the graph as follows. Let be a finite set of unknown elements and let be a set of all ordered pair of V. Each relation defined on the set V is an arbitrary subset so that n = |G| is the size of a graph. The relation E is symmetric if and is reflexive if. Therefore, we able to define a simple graph as G (V, E) where V is a finite set of nodes (vertices) and E is a reflexive relation on the set V and it is known as the link (edge) of graph G. In this paper, we study the simple unweighted non-oriented graphs, which contain no self-loops or multiple edges. When we use the term ‘graph’ we mean a simple graph, otherwise, we point out explicitly. G (n, m) is a set of all graphs that have n nodes and m edges. In a non-oriented graph, the relation E is asymmetric.

Reflexive relation

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The impact of node arrival process and stochastic edge growth on scale-free distribution in complex networks