# Mathematics

#### Path-based strong component algorithm ^{}

In graph theory, the strongly connected components of a directed graph may be found using an algorithm that uses depth-first search in combination with two stacks, one to keep track of the vertices in the current component and the second to keep track of the current search path.

#### Strongly connected component ^{}

In the mathematical theory of directed graphs, a graph is said to be strongly connected or diconnected if every vertex is reachable from every other vertex.

#### Directed graph ^{}

In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is a set of vertices connected by edges, where the edges have a direction associated with them.

#### Loop (graph theory) ^{}

In graph theory, a loop (also called a self-loop or a "buckle") is an edge that connects a vertex to itself. A simple graph contains no loops. For an undirected graph, the degree of a vertex is equal to the number of adjacent vertices.

#### Cycle (graph theory) ^{}

In graph theory, a cycle is a path of edges and vertices wherein a vertex is reachable from itself. There are several different types of cycles, principally a closed walk and a simple cycle; also, e.g., an element of the cycle space of the graph.

#### Graph theory ^{}

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines).

#### The violent attack that turned a man into a maths genius ^{}

BBC Future has brought you in-depth and rigorous stories to help you navigate the current pandemic, but we know that’s not all you want to read. So now we’re dedicating a series to help you escape.

#### The maths problem that could bring the world to a halt ^{}

It’s not easy to accurately predict what humans want and when they will want it. We’re demanding creatures, expecting the world to deliver speedy solutions to our increasingly complex and diverse modern-day problems.

#### Mandelbrot set ^{}

The Mandelbrot set is the set of complex numbers c {\displaystyle c} for which the function f c ( z ) = z 2 + c {\displaystyle f_{c}(z)=z^{2}+c} does not diverge when iterated from z = 0 {\displaystyle z=0} , i.e.

#### The myth of being 'bad' at maths ^{}

Are you a parent who dreads having to help with maths homework? In a restaurant, do you hate having to calculate the tip on a bill? Does understanding your mortgage interest payments seem like an unsurmountable task? If so, you’re definitely not alone.

#### Solving the Three Body Problem ^{}

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