One of the most effective ways to present data and uncover insights
We like Oppenheimer, but theory in data structures and algorithms will not just take you so far. Understanding the fundamentals is crucial, but applying these concepts to solve real-world problems is where the true power lies.
In computer science, graphs are incredibly versatile structures that represent a set of objects and the connections between them. These objects are called nodes or vertices, and the connections are known as edges. Graphs can model a variety of systems in diverse fields, such as social networks, communication networks, biological networks, and more.
As was mentioned earlier, a graphs is any collection of nodes and connections between those nodes.
If we were to represent it visually, it would look something like that:
In graphs, edges can be either directed or undirected. Directed edges mean you can only move in one direction. For example, if there's a directed edge from node A to node B, you can go from A to B, but not fromB to A.
In diagrams, directed edges are shown as arrows. Undirected edges, on the other hand, allow movement in both directions, so you can travel fromA to B andB to A. These edges are represented as simple lines between nodes.
In binary trees, for instance, the edges were directed. Binary trees are directed graphs. You can't access a node's parent, only its children. Once you move to a child, you can't move back.
Another key concept is the connected component. A connected component in a graph is a set of nodes that are interconnected by edges.
For instance, in binary trees, there must be only one connected component, meaning all nodes must be reachable from the root node.
A node can have multiple edges attached to it. In a directed graph, a node can have numerous edges entering and leaving it. The number of edges that can reach the node is called its indegree, while the number of edges that can leave the node is called its outdegree. Nodes connected by an edge are referred to as neighbors. For instance, in a graph like A <-> B <-> C, A and B are neighbors, B is a neighbor to both A and C, and C is a neighbor to B.