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Math Equations

In: Computers and Technology

Submitted By jodidell
Words 490
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Often, networks have certain attributes that can be calculated to analyze the properties & characteristics of the network. These network properties often define network models and can be used to analyze how certain models contrast to each other. Many of the definitions for other terms used in network science can be found in Glossary of graph theory.
Density[edit]
The density of a network is defined as a ratio of the number of edges to the number of possible edges, given by the binomial coefficient , giving Another possible equation is , whereas the ties are unidirectional (Wasserman & Faust 1994)[2]. This gives a better overview over the network density, because unidirectional relationships can be measured.
Size[edit]
The size of a network can refer to the number of nodes or, less commonly, the number of edges which can range from (a tree) to (a complete graph).
Average degree[edit]
The degree of a node is the number of edges connected to it. Closely related to the density of a network is the average degree, . In the ER random graph model, we can compute where is the probability of two nodes being connected.
Average path length[edit]
Average path length is calculated by finding the shortest path between all pairs of nodes, adding them up, and then dividing by the total number of pairs. This shows us, on average, the number of steps it takes to get from one member of the network to another.
Diameter of a network[edit]
As another means of measuring network graphs, we can define the diameter of a network as the longest of all the calculated shortest paths in a network. In other words, once the shortest path length from every node to all other nodes is calculated, the diameter is the longest of all the calculated path lengths. The diameter is representative of the linear size of a network.
Clustering coefficient[edit]
The clustering coefficient is a measure of an "all-my-friends-know-each-other" property. This is sometimes described as the friends of my friends are my friends. More precisely, the clustering coefficient of a node is the ratio of existing links connecting a node's neighbors to each other to the maximum possible number of such links. The clustering coefficient for the entire network is the average of the clustering coefficients of all the nodes. A high clustering coefficient for a network is another indication of a small world.
The clustering coefficient of the 'th node is where is the number of neighbours of the 'th node, and is the number of connections between these neighbours. The maximum possible number of connections between neighbors is, of course,

Answer the following questions:
1. Is the graph of the equation the graph of a function? Yes it is
2. What is the domain and range of this relationship? To be honest I am not sure
3. Does the inverse exist? No it dows not

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