May 8, 2013 · The example cited is the adjacency matrix for a disconnected graph (nodes 1&2 are connected, and nodes 3&4 are connected, but neither pair is connected to the other pair). When you calculate A^2, the answer (as stated) is the identity matrix.

Aug 27, 2015 · $\begingroup$ Take a small adjacency matrix and by hand work out an algorithm to figure out which nodes are reachable from which other nodes. $\endgroup$ – NovaDenizen Commented Aug 27, 2015 at 6:41

Mar 9, 2013 · The next method creates a matrix of two dimensions, n by n, where n is the number of node we get from the graph class. Foreach of the nodes, we search if they have a link, if they have a link, a filled the matrix in the appropriate position.

Sep 16, 2015 · An adjacency matrix keeps a value (1/0) for every pair of nodes, whether the edge exists or not, so it requires n*n space. An adjacency list only contains existing edges, so its length is at most the number of edges (or the number of nodes in case there are fewer edges than nodes).

Dec 7, 2014 · and finally an image test.png (note that your adjacency matrix lists a connection of the first item with itself, which shows as the loop at node A): As a more complex example, you could plot a bucky-ball as in the documentation of gplot :

Note that this description of the adjacency matrix makes the connection between powers of the adjacency matrix and paths on the graph immediate. Said another way, there is a category called the category of spans of sets , and a graph may be regarded as an endomorphism in this category.

Mar 27, 2013 · A adjacency matrix presents connections between nodes in a arbitrary tree. Here is a instance of adjacency matrix which presents a undirected graph: 1 2 3 4 1 0 1 1 0 ...

Apr 6, 2015 · #Graph using adjacency matrix class GraphAM: #no of vertices __n=0 #adjacency matrix of size 10x10 initialize with 0 __g=[[0 for column in range(10)]for row in range(10)] __listofVertex=[] def __init__(self,vertex): #adding a vertex in a list self.__listofVertex.append(vertex) #saving no of vertices self.__n=len(self.__listofVertex) #updating ...

Jul 25, 2013 · If we multiply an adjacency matrix A[][] by itself we get A^2(say AM2) whose each vertex A[i][j] basically represents the number of paths of path length 2 from i to j. Similarly,If we multiply an adjacency matrix 3 times i.e we get A^3(say AM3) whose each vertex A[i][j] basically represents the number of paths of path length 3 from i to j.. and ...

Apr 28, 2017 · What do you think is the most efficient algorithm for checking whether a graph represented by an adjacency matrix is connected? In my case I'm also given the weights of each edge. There is another question very similar to mine: How to test if a graph is fully connected and finding isolated graphs from an adjacency matrix