Unformatted text preview: is connected (i.e.,
ignoring the directions of edges).
strongly connected if each node can reach every other node by a
1 2 3 Figure: A directed graph that is connected but not strongly connected
10 Networks: Lecture 2 Graphs Trees, Stars, Rings, Complete and Bipartite Graphs
A tree is a connected (undirected) graph with no cycles.
A connected graph is a tree if and only if it has n − 1 edges.
In a tree, there is a unique path between any two nodes. Complete graph Ring Star Bipartite graph Tree actors movies
11 Networks: Lecture 2 Graphs Neighborhood and Degree of a Node
The neighborhood of node i is the set of nodes that i is connected to.
For undirected graphs:
The degree of node i is the number of edges that involve i (i.e.,
cardinality of his neighborhood). For directed graphs:
Node i ’s in-degree is ∑j gji .
Node i ’s out-degree is ∑j gij .
1 2 4 3 Figure: Node 1 has in-degree 1 and out-degree 2
12 Networks: Lecture 2 Properties of Networks Properties of Networks
While a small network can be visualized directly by its graph (N , g ),
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- Fall '09
- Graph Theory, Graph Theory and Social Networks