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Can anyone suggest me good online tutorials on Graph Theory ie BFS,DFS and other related Graph algos?
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A path is closed if the first vertex is the same as the last vertex (i.e., it starts and ends at the same vertex.) A cycle is a simple closed path. Note: a cycle is not a simple path.
The concept of graphs in graph theory stands up on some basic terms such as point, line, vertex, edge, degree of vertices, properties of graphs, etc.
A walk is said to be open if the first and the last vertices are different i.e. the terminal vertices are different. A walk is said to be closed if the first and last vertices are the same. That means you start walking at a vertex and end up at the same.
Graph theory is a branch of mathematics which is concerned with the study of 'graphs', which are mathematical representations of objects and their relationships. The graph is a collection of points (referred to as nodes or vertices) connected by lines (referred to as edges).
If you like coding in python, you may check the book:
Algorithmic Graph Theory
The book is GNU-FDL licensed, which means you can read and download all the content for free. And all the source code in the book are provided for Sage. Sage is a open source alternative of Matlab. As Sage use python as it's language to write scripts, all source code in Sage are essentially python code with additional modules (from sage).
ps: This Algorithmic Graph Theory is totally a different thing from @Elias's Algorithmic Graph Theory.
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My recommendations:
Introductory - JMT Patrick:
http://www.youtube.com/watch?v=HmQR8Xy9DeM
Moderately difficult lectures - ADUni and Berkeley:
http://aduni.org/courses/algorithms/index.php?view=cw
http://www.cs.berkeley.edu/~blum/174notes.html
Advanced stuff - MIT:
http://ocw.mit.edu/courses/mathematics/18-315-combinatorial-theory-introduction-to-graph-theory-extremal-and-enumerative-combinatorics-spring-2005/
As a bonus, great presentation from Neo CEO:
http://www.youtube.com/watch?v=UodTzseLh04&feature=related
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