I will be programming out the latter today. However, it is also commonly used today to find the shortest paths between a source node and all other nodes. Dijkstra’s algorithm was originally designed to find the shortest path between 2 particular nodes.Major stipulation: we can’t have negative edge lengths.Dijkstra’s Algorithm, Ho!īefore we jump right into the code, let’s cover some base points. If I wanted my edges to hold more data, I could have the adjacency matrix hold edge objects instead of just integers. In this way, the space complexity of this representation is wasteful. You will also notice that the main diagonal of the matrix is all 0s because no node is connected to itself. it is a symmetric matrix) because each connection is bidirectional. Because the graph in our example is undirected, you will notice that this matrix is equal to its transpose (i.e. A “0” element indicates the lack of an edge, while a “1” indicates the presence of an edge connecting the row_node and the column_node in the direction of row_node → column_node. As such, each row shows the relationship between a single node and all other nodes. Each element at location represents an edge. In our case, row 0 and column 0 will be associated with node “A” row 1 and column 1 with node “B”, row 3 and column 3 with “C”, and so on. Each row is associated with a single node from the graph, as is each column. If you want to learn more about implementing an adjacency list, this is a good starting point.īelow is the adjacency matrix of the graph depicted above. Let’s quickly review the implementation of an adjacency matrix and introduce some Python code. Either implementation can be used with Dijkstra’s Algorithm, and all that matters for right now is understanding the API, aka the abstractions (methods), that we can use to interact with the graph. I will be showing an implementation of an adjacency matrix at first because, in my opinion, it is slightly more intuitive and easier to visualize, and it will, later on, show us some insight into why the evaluation of our underlying implementations have a significant impact on runtime. Each has their own sets of strengths and weaknesses.
The two most common ways to implement a graph is with an adjacency matrix or adjacency list. This step is slightly beyond the scope of this article, so I won’t get too far into the details. Graphs have many relevant applications: web pages (nodes) with links to other pages (edges), packet routing in networks, social media networks, street mapping applications, modeling molecular bonds, and other areas in mathematics, linguistics, sociology, and really any use case where your system has interconnected objects. the string “Library”), and the edges could hold information such as the length of the tunnel. For example, if this graph represented a set of buildings connected by tunnels, the nodes would hold the information of the name of the building (e.g. There also exist directed graphs, in which each edge also holds a direction.īoth nodes and edges can hold information.
Depicted above an undirected graph, which means that the edges are bidirectional.
A node is just some object, and an edge is a connection between two nodes.
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