Matrix Representation Of Graph

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Matrix Representation Of Graph

  1. 1. Presented By:Abhishek PachisiaB.Tech-IT(V Sem) 090102801
  2. 2. Graph is a set of edges and vertices.Graph can be represented in the form of matrix.Different matrix that can be formed are: 1. Incidence Matrix 2. Adjacency Matrix 3. Cut-Set Matrix 4. Circuit Matrix 5. Path Matrix
  3. 3. Edge connected to the vertex is known as incidence edge to that vertex.If vertex is incident on vertex then put 1 else 0. Vertex Edges 1 a, b 2 a, b, c, f aij =1, if edge ej is incident on vertex vi 3 c, d, g =0, otherwise 4 d, e 5 d, e, f, g, h 6 h V1 a V6 V2 f V5 h b Edges a b c d e f g h V1 1 1 0 0 0 0 0 0 V2 1 1 1 0 0 1 0 0 Vertex c e V3 0 0 1 1 1 0 1 0 V4 0 0 0 1 1 0 1 0 V5 0 0 0 1 1 1 1 1 V6 0 0 0 0 0 0 0 1 V3 d V4
  4. 4.  If two vertices are connected by single path than they are known as adjacent vertices. If vertex is connected to itself then vertex is said to be adjacent to itself.If vertex is adjacent then put 1 else 0. V1 a V6 V2 f V5 h Vertices b V1 V2 V3 V V5 V6 4 V1 0 1 0 0 0 0 V2 1 0 1 0 1 0 Vertices c e V3 0 1 0 1 1 0 V4 0 0 1 1 1 0 V5 0 1 1 1 0 1 V6 0 0 0 0 0 1 V3 d V4
  5. 5. Cut set is a “Set of edges in a graph whose removal leaves the graph disconnected”.If edge of graph is a part of given cut set then put 1 else 0. Cut Set Edges Cij =1, if jth cutset contains edge 1 f, g, d =0, otherwise 2 c, g, e 3 h V1 a V6 4 a, b V2 f V5 h b Edges a b c d e f g h 1 0 0 0 1 0 1 1 0 Cut Sets c e 2 0 0 1 0 1 0 1 0 3 0 0 0 0 0 0 0 1 4 1 1 0 0 0 0 0 0 V3 d V4
  6. 6. Circuit can be defined as “A close walk in which no vertex/edge can appear twice”.If edge of graph is a part of given circuit then put 1 else 0. Circuit Edges Cij =1, if circuit contains edge 1 d, e, g =0, otherwise 2 c, f, g 3 c, d, e, f V1 a V6 4 a, b V2 f V5 h b Edges a b c d e f g h 1 0 0 0 1 1 0 1 0 Circuits c e 2 0 0 1 0 0 1 1 0 3 0 0 1 1 1 1 0 0 4 1 1 0 0 0 0 0 0 V3 d V4
  7. 7. Path can be defined as “A open walk in which no vertex/edge can appear twice”.If edge of graph is a part of given path then put 1 else 0. Path Edges 1 a, f, h P( Vj,Vi)=1,if edge is on path Ex: P ( V1,V6) 2 a, c, g, h =0, otherwise 3 a, c, d, e, h 4 b, f, hV1 a V6 5 b, c, g, h 6 b,c, d, e, h V2 f V5 h Edges b a b c d e f g h 1 1 0 0 0 0 1 0 1 0 Paths c e 2 1 1 0 0 0 1 1 3 1 0 1 1 1 0 0 1 4 0 1 0 0 0 1 0 1 5 0 1 1 0 0 0 1 1 6 0 1 1 1 1 0 0 1 V3 d V4

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