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Sem 5 Prep
← Visual AnalyticsNodes, edges and the shape of a network

Formulas for this chapter

Density (undirected)

Density = e / (n(n-1)/2)

Whenever a question asks how connected an undirected network is overall. Count the edges first, and check with sum of degrees = 2e.

e
Number of edges actually present
n
Number of nodes, including singletons
n(n-1)/2
Maximum possible edges if every node joined every other

Density (directed)

Density = e / (n(n-1))

For a directed network, where each pair can be joined in both directions, so the maximum is twice the undirected one. Say which formula you are using; the two answers differ by exactly a factor of 2.

e
Number of directed edges (arrows)
n
Number of nodes
n(n-1)
Maximum possible directed edges

Degree sum check

SUM of degrees = 2e (undirected) · SUM in-degrees = SUM out-degrees = e (directed)

After counting edges or degrees, before any centrality arithmetic. It catches a missed or double-counted edge in one line.

degree
Number of edges at a node
e
Number of edges in the network
Step 3 of 27
The real wordsTheory

Social Network Analysis

Social Network Analysis (SNA)A method used to perform visual and mathematical analysis on relationships. The analysis is visually interesting and mathematically rigorous.

It is used for people, concepts, literature, biological systems and electronic systems such as computers. Its two questions: how are systems connected, and how can we explain networks through mathematical models.

Notice the "and". A pretty graph with no numbers is not SNA, and a table of numbers with no picture is not either.

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