42 lines
1.6 KiB
Markdown
42 lines
1.6 KiB
Markdown
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## Graph
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Graph is a useful data structure for representing most of the real world problems involving a set of users/candidates/nodes and their relations. A Graph consists of two parameters :
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```
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V = a set of vertices
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E = a set of edges
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```
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Each edge in `E` connects any two vertices from `V`. Based on the type of edge, graphs can be of two types:
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1. **Directed**: The edges are directed in nature which means that when there is an edge from node `A` to `B`, it does not imply that there is an edge from `B` to `A`.
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An example of directed edge graph the **follow** feature of social media. If you follow a celebrity, it doesn't imply that s/he follows you.
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2. **Undirected**: The edges don't have any direction. So if `A` and `B` are connected, we can assume that there is edge from both `A` to `B` and `B` to `A`.
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Example: Social media graph, where if two persons are friend, it implies that both are friend with each other.
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### Representation
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1. **Adjacency Lists**: Each node is represented as an entry and all the edges are represented as a list emerging from the corresponding node. So if vertex `1` has eadges to 2,3, and 6, the list corresponding to 1 will have 2,3 and 6 as entries. Consider the following graph.
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```
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0: 1-->2-->3
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1: 0-->2
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2: 0-->1
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3: 0-->4
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4: 3
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```
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It means there are edges from 0 to 1, 2 and 3; from 1 to 0 and 2 and so on.
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2. **Adjacency Matrix**: The graph is represented as a matrix of size `|V| x |V|` and an entry 1 in cell `(i,j)` implies that there is an edge from i to j. 0 represents no edge.
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The mtrix for the above graph:
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```
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0 1 2 3 4
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0 0 1 1 1 0
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1 1 0 1 0 0
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2 1 1 0 0 0
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3 1 0 0 0 1
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4 0 0 0 1 0
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```
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