In Mathematics and Computer Science, the graph theory is just the theory of graphs basically overall. It's basically the relationship between objects. The nodes are just lines that connects the graph. There are a total of six nodes in a family branch tree for a graph theory basically.
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A spanning tree is a tree associated with a network. All the nodes of the graph appear on the tree once. A minimum spanning tree is a spanning tree organized so that the total edge weight between nodes is minimized.
That depends how the data is stored. If you use predesigend classes to store information about nodes and edges, check the documentation of the specific class or classes. Or ask a question here, specifiying the class you are using.
Assuming that the voltage between two nodes are the same, current changes with branches. If you add branches, this means the current will be divided, depending on the resistance strength. Greater the resistance, the lower the current. If there is no resistance, it will end up in a short circuit, getting all the current. If there is great resistance, there will be very little current passing. Mathematically, V=I*R is the formula. If you know the voltage between two nodes, you can calculate the currency (I) in each branch and for the whole nodes by putting in the particular resistance value for the branch or the whole nodes.
We use the term balance when referring to balanced binary trees. These are typically implemented using red/black trees, thus ensuring every parent node has as many nodes under the left branch as it has under the right branch.
it is a part of the stem from which a branch grows
In the area known as graph theory, a tree has nodes and edges joining the nodes. A tree is a type of graph which is connected (you can get from each node to every other node by following the edges), but has no cycles (you can't follow edges around in a circle). There is more, including a picture, here: http://en.wikipedia.org/wiki/Tree_(graph_theory) Trees have uses in computer science.
It's a set of nodes, together with edges that have directions associated with them.
The number of triangles in a complete graph with n nodes is n*(n-1)*(n-2) / 6.
Use a simple DFS/BFS traversal. If you have gone through all nodes, the graph is connected.
Graph theory - a mathematical circuit requires a)transportation between nodes (points) b) w/o returning to the original node via a line segment already used. The most simplistic circuit in math would be three nodes (a triangle, containg six unique pathways). One line seg (2 nodes) has 2 pathways but both violate b) QED
Sparse vs. Dense GraphsInformally, a graph with relatively few edges is sparse, and a graph with many edges is dense. The following definition defines precisely what we mean when we say that a graph ``has relatively few edges'': Definition (Sparse Graph) A sparse graph is a graph in which .For example, consider a graph with n nodes. Suppose that the out-degree of each vertex in G is some fixed constant k. Graph G is a sparse graph because .A graph that is not sparse is said to be dense:Definition (Dense Graph) A dense graph is a graph in which .For example, consider a graph with n nodes. Suppose that the out-degree of each vertex in G is some fraction fof n, . E.g., if n=16 and f=0.25, the out-degree of each node is 4. Graph G is a dense graph because .
one larger than the number
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In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other.A planar graph already drawn in the plane without edge intersections is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point in 2D space, and from every edge to a plane curve, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points. Plane graphs can be encoded by combinatorial maps.Example of Planner graphButterfly Graph.
A spanning tree is a tree associated with a network. All the nodes of the graph appear on the tree once. A minimum spanning tree is a spanning tree organized so that the total edge weight between nodes is minimized.
They are located near branch of bronchial tree where it splits to left and right lungs.