A graph is a pictorial representation of a set of objects where some pairs of objects are connected by links. The interconnected objects are represented by points termed as vertices, and the links that connect the vertices are called edges. Mathematical graphs can be represented in data structure

BFS algorithm. ?L 0 = { s}. ?L 1 Lemma. Let G be a connected graph, and let L 0, , L k be the layers produced by BFS starting at node s ? graph connectivity and graph traversal ? testing bipartiteness ? connectivity in directed graphs Graph algorithms, breadth-first search, depth-first search, shortest path, arbitrage, strongly connected components 4.5 (628 ratings) Course Ratings are calculated from individual students' ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately. Co-training and Multiview Algorithms Manifold Regularization and Graph-Based Algorithms S3VMs and Entropy Regularization 2 Part II Theory of SSL Online SSL Multimanifold SSL Human SSL Xiaojin Zhu (Univ. Wisconsin, Madison) Tutorial on Semi-Supervised Learning Chicago 2009 3 / 99 algorithm to find an Euler path in an Eulerian graph. CONSTRUCT Input: A connected graph G = (V, E) with two vertices of odd degree. Output: The graph with its edges labeled according to their order of appearance in the path found. 1 Find a simple cycle in G. 2 Delete the edges belonging in C. 3 Apply algorithm to the remaining graph. Considering a graph, there will be many links within a cluster, and fewer links between clusters. This means if you were to start at a node, and then randomly travel to a connected node, you're more likely to stay within a cluster than travel between. This is what MCL (and several other clustering algorithms) is based on. - Eulerian graph detection - Semi-Eulerian graph detection - Tarjan's algorithm for strongly connected components in directed graphs - Tree detection - Bipartite graph detection