Simple graph |
There are at most one edge between a pair of nodes. |

Multi graph |
There are more than one edge between a pair of nodes. Contain self-loop, which means the two heads of an edge may connecting to same node. |

Connected Graph |
For each pair of nodes, a path exists between them. |

Directed Graph |
The connection between two nodes is only one-way relationship. |

Strong Connected Graph |
In a directed graph. For any pairs of nodes A and B. There are paths from A to B and fromB to A. |

Tree |
A graph is connected and doesn’t contain any cycle. |

Weight Graph |
Every edges in the graph have been assigned a number, which are the weight of that edges. |

Planar Graph |
A graph that can be embebbed on the plane with no edges cross each other |

Bipartite Graph |
A graph that nodes can be divided into two disjoint sets such that no edge connects the nodes in the same set. |