Graphs and Networks Definitions 0.0 / 5 ? Further MathsGraphs and NetworksA2/A-levelOCR Created by: Sarah123Created on: 14-07-17 10:08 Trail Sequence of arcs such that the end node of one is the start node of the next 1 of 14 Path A trail but with the restriction that no node is passed through more than once 2 of 14 Closed Trail Initial and final nodes are the same 3 of 14 Cycle Closed path where only the initial and last nodes are the same 4 of 14 Order of a Node / Valency number of arcs meeting at the same node 5 of 14 Connected Graph For any two nodes, a path can be found connecting the nodes 6 of 14 Simple Graph A graph without loops and multiple arcs 7 of 14 Complete Graph Every node is connected to every other node by just one arc 8 of 14 Eulerian Graph A connected graph which has a closed trail containing every arc precisely once 9 of 14 Semi-Eulerian Graph A connected graph where precisely 2 nodes have an odd order 10 of 14 Weighted Graph A graph whose arcs have a value 11 of 14 Digraph A graph whose arcs have a direction 12 of 14 Tree A connected graph with no cycles 13 of 14 Spanning Tree A connected graph which includes all the nodes in a network 14 of 14
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