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# Path a path is a sequence of nodes and e and

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Unformatted text preview: The degree of a node i, deg(i), is the number of arcs incident to i. – For directed graphs, in-degree and out-degree, indeg(i) and outdeg(i), are the number of arcs pointing into and out of i, respectively. • Path – A path is a sequence of nodes { , , ,…, } and ) ∈E and no nodes are relevant arcs such that ( , repeated. Graphs and Networks • Cycle – A cycle is a path + the edge ( , • Connected Network ). – G is a connected network if a path exists between any pair of nodes. • Tree – A tree is a graph without cycles. • Spanning Tree – A spanning tree is a connected subgraph that includes all nodes and is a tree. – Example: Minimum Spanning Tree • Minimum spanning tree (MST) problem – Among all the spanning trees of a weighted (cost) and connected graph G= (N, E), – Find the one (or possibly more) with the least total weight. • Kruskal's Algorithm 1. 2. 3. Let edge set E0 = Φ. Find the cheapest edge (i,j) in the graph (if there is more than one, pick one at random) and include...
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