Graph Theory and Ecology By Ojasvi Khanna

Introduction to Graph Theory Given by Leonhard Euler After solving the problem of Seven Bridges of Königsberg

Important Terms Vertices/ Nodes/ Points

Important Terms Vertices/ Nodes/ Points V = {A, B, C, D, E, F} Cardinality = # vertices =

Important Terms Vertices/ Nodes/ Points V = {A, B, C, D, E, F} Cardinality = # vertices = 6

Important Terms Vertices/ Nodes/ Points Edges V = {A, B, C, D, E, F} Cardinality = # vertices = 6 Degree of vertice = # edges it has

Important Terms Vertices/ Nodes/ Points Edges V = {A, B, C, D, E, F} Cardinality = # vertices = 6 Degree of vertice = # edges it has A = B = C = D = E = F =

Important Terms Vertices/ Nodes/ Points Edges V = {A, B, C, D, E, F} Cardinality = # vertices = 6 Degree of vertice = # edges it has A = 2 B = 2 C = 2 D = 3 E = 3 F = 2

Ecosystems A biological community of organisms interacting with the biotic and abiotic elements in the environment. Can also be seen as a network of interactions

Ecological Networks Ecosystems can be seen as ecological networks to help us visualise: Species Richness Food Webs Transfer of Energy Population Density Ecological Importance

Examples of Ecological Network Node = Species Edge = Energy Transfer through eating

Size of node = Population Density Cardinality = Species Richness Degree of node = Importance of species in ecosystem

Significance A higher degree of any species in an ecological network shows that it is of high ecological importance Removing one ecologically important species = collapse of the network Representation of biodiversity Allow visualisation of importance of a species

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