What makes a graph connected

Computer Organization. Discrete Mathematics. Ethical Hacking. Computer Graphics. Software Engineering. Web Technology. Cyber Security. C Programming. Control System. Data Mining. Data Warehouse. Javatpoint Services JavaTpoint offers too many high quality services. It defines whether a graph is connected or disconnected. Without connectivity, it is not possible to traverse a graph from one vertex to another vertex.

A graph is said to be connected graph if there is a path between every pair of vertex. From every vertex to any other vertex there must be some path to traverse. This is called the connectivity of a graph. A graph is said to be disconnected, if there exists multiple disconnected vertices and edges.

Graph connectivity theories are essential in network applications, routing transportation networks, network tolerance etc. Example In the above example, it is possible to travel from one vertex to another vertex. Example In the above example, it is not possible to traverse from vertex B to H because there is no path between them directly or indirectly.

Let's see some basic concepts of Connectivity. Cut Vertex A single vertex whose removal disconnects a graph is called a cut-vertex. Note: Let G be a graph with n vertices: A connected graph G may have maximum n-2 cut vertices. Removing a cut vertex may leave a graph disconnected. Removing a vertex may increase the number of components in a graph by at least one.

Every non-pendant vertex of a tree is a cut vertex. Example 1 Example 2 In the above graph, vertex 'e' is a cut-vertex. Cut Edge Bridge A cut- Edge or bridge is a single edge whose removal disconnects a graph. Note: Let G be a graph with n vertices: A connected graph G may have at most n-1 cut edges. Removing a cut edge may leave a graph disconnected. Find a minimum spanning tree between these centroids on this new graph. Now connect the components along the minimum spanning tree.

However, this algorithm could tell you to connect components that cannot be connected eg imagine a graph consisting of three concentric components - you will not be able to connect the outer to the inner. So this can only be a heuristic suggestion. It might be better just to always connect a component to the other one that has the nearest nodes. Like i said in the comment it can be done by finding the connected components using a dfs traversal, then taking the endpoints of the components and joining the components, so we know that the edges will be minimum i.

How are we doing? Please help us improve Stack Overflow. Take our short survey. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Collectives on Stack Overflow. Learn more. Algorithm to make undirected graph be connected Ask Question. Asked 5 years, 8 months ago. Active 5 years, 8 months ago. Viewed 2k times. Improve this question. Colud you elaborate more on the statement "I don't want to add edges which cross over other edges".

I think it can be done by finding connected components in the graph and then taking the endpoints, of those components and forming edges. The issue is that that new edge might intersect in the algebraic sense another, already existing edge, which I want to avoid. Note that my nodes and edges all have Cartesian coordinate positions so I can easily define the notion of edge intersection in that case.

Add a comment. Take a look at the following graph. By removing two minimum edges, the connected graph becomes disconnected. Graph Theory - Connectivity Advertisements. Previous Page. Next Page. Previous Page Print Page. Save Close. Dashboard Logout.