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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 arcs, links or lines ). A distinction is made between undirected graphs, where edges link ...
In the mathematical area of graph theory, a clique ( / ˈkliːk / or / ˈklɪk /) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent. That is, a clique of a graph is an induced subgraph of that is complete. Cliques are one of the basic concepts of graph theory and are used in many ...
e. A biological network is a method of representing systems as complex sets of binary interactions or relations between various biological entities. [1] In general, networks or graphs are used to capture relationships between entities or objects. [1]
Component (graph theory) In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself connected has exactly one component, consisting of the ...
Network motifs are recurrent and statistically significant subgraphs or patterns of a larger graph. All networks, including biological networks, social networks, technological networks (e.g., computer networks and electrical circuits) and more, can be represented as graphs, which include a wide variety of subgraphs.
1. A book, book graph, or triangular book is a complete tripartite graph K1,1,n; a collection of n triangles joined at a shared edge. 2. Another type of graph, also called a book, or a quadrilateral book, is a collection of 4 -cycles joined at a shared edge; the Cartesian product of a star with an edge. 3.
Evolutionary graph theory is an area of research lying at the intersection of graph theory, probability theory, and mathematical biology. Evolutionary graph theory is an approach to studying how topology affects evolution of a population. That the underlying topology can substantially affect the results of the evolutionary process is seen most ...
A polytree. In mathematics, and more specifically in graph theory, a polytree [1] (also called directed tree, [2] oriented tree [3] or singly connected network [4]) is a directed acyclic graph whose underlying undirected graph is a tree. In other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that ...