Structural Analysis

Graph Degrees

The Degree of a vertex quantifies its connectivity within the network. In directed graphs, we track In-degree (incoming signals) and Out-degree (outgoing signals) independently.

Handshaking LemmaΣ deg(v) = 2|E|

Directed SumΣ d⁻ = Σ d⁺

In-Degree (d⁻)

The number of edges directed towards a vertex. It represents the number of "prerequisites" or incoming dependencies.

Out-Degree (d⁺)

The number of edges originating from a vertex. It represents the "influence" or reach of that node.

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