What are graphs?

Graphs are non-linear data structures made up of nodes connected by edges. More formally a Graph is composed of a set of vertices( V ) and a set of edges( E ). The graph is denoted by G(E, V).


Weight: A weight can be assigned to an edge, representing the cost or distance between two vertices. A weighted graph is a graph where the edges have weights.

Degree: The degree of a vertex is the number of edges that connect to it. In a directed graph, the in-degree of a vertex is the number of edges that point to it, and the out-degree is the number of edges that start from it.

Path: A path is a sequence of vertices that are connected by edges. A simple path does not contain any repeated vertices or edges.

Cycle: A cycle is a path that starts and ends at the same vertex. A simple cycle does not repeat a node or an edge

Connectedness: A graph is said to be connected if there is a path between any two vertices. The opposite of a connected graph is called disconnected.

Planarity: A graph is planar if it can be drawn without any edges crossing each other.

Bipartiteness: A graph is said to be bipartite if its vertices can be divided into two disjoint sets such that no two vertices in the same set are connected by an edge.

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