Networks - Basic terms defined

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Networks - Basic terms.
Summary and concepts.

Network	A network is a group or system of interconnected objects. A network can be represented as a diagram of connected lines (called edges) and points (called vertices). Examples of networks include the route a bus might follow or the route a person might take to do a letter box drop.

Vertex or node	An activity or a stage in a network diagram. A vertex in a network diagram is a point representing: an activity; or the time when an activity has been completed. In the above diagram, the vertices describe the action taking place. The arrows show what the next action will be. In the second diagram above, the action is written along the arrow (called an edge) and the action is regarded as taking place between the vertices (shown as black dots). Both diagrams can be used: the former diagram is more commonly used in the work environment; the second diagram is more common in school contexts. You can use either - and you must be able to interpret both representations. Lines or pathways (i.e. edges) of the network intersect or branch out from a vertex. A vertex is also frequently referred to as a node.
Degree of a vertex	The number of edges coming into the vertex.
Edge	The line joining two vertices to each other. An edge could be curved and it is then described as an arc rather than a line.
Directed edges	Edges with an arrow to show the direction of the activity.
Weighted edges	Edges with a number indicating time, cost, distance, etc.

Path.	A path in a network diagram is a trail in which there are no repeated vertices (and of course where all of the edges are distinct). An open path starts and finishes at different vertices. A closed path - called a cycle - starts and finishes at the same vertex. There may be multiple paths between the same two vertices.
Trail	A walk with no repeated edges. A circuit is a closed trail.
Walk.	Any route along the edges of a network. Edges and vertices can be repeated.
Flow.	The number or amount of a quantity flowing through a system or network - either through a part of the network or through the entire network.

Connected network	A connected network has a path between any two vertices. Often this path will span a number of vertices.
Degree of a vertex.	The number of edges connected to a given vertex. An even vertex has an even number of edges connected to it. An odd vertex has an odd number of edges connected to it.
(Total) degrees in a network.	The sum of the degrees of all vertices in a network equals twice the number of edges - each edge has two vertices. Hence the sum of the degrees in a network is always even.
Directed network	A network in which the edges between vertices only flow in the direction indicated. We read these as FROM ... TO ....
Weighted network.	A network in which the edges between vertices also have a value to indicate the amount of the characteristic required or involved. A weight could be: a quantity flowing through the network (for example the amount of water flowing through that part of the network); a cost of that part of the network (i.e. the cost to complete that activity); the time taken to complete that part of the network (i.e. to complete that edge). The weight of a network is the sum of the weights along all edges.