# neighbour list vs adjacency matrix

However, • Adjacency List Representation – O(|V| + |E|) memory storage – Existence of an edge requires searching adjacency list – Define degree to be the number of edges incident on a vertex ( deg(a) = 2, deg(c) = 5, etc. Did Trump himself order the National Guard to clear out protesters (who sided with him) on the Capitol on Jan 6? To find if a vertex has a neighbor, we need to go through the linked list of the vertex. }$$ If $p = \frac{E}{N^2}$ is the probability that an edge is present, the entropy is $- \log_2{p(1-p)}$. a list is really just a single column matrix!!! If we use balanced binary search trees, it becomes $O(1 + \log(deg(V))$ and using appropriately constructed hash tables, the running time lowers to $O(1)$. I now consider two standard data structures: Adjacency Matrix. Thus we usually don't use matrix representation for sparse graphs. Undirected No Weights Undirected Weighted Directed No Weights Directed Weighted. But if we use adjacency list then we have an array of nodes and each node points to its adjacency list containing ONLY its neighboring nodes. I personally prefer to use a hash table and I am using the hash table in my implementation. Neighbour : Down State : When interface is down or no neighbour is there . To answer by providing a simple analogy.. Next create an adjacency matrix that represents the graph. If there is an edge between vertices $A$ and $B$, we set the value of the corresponding cell to 1 otherwise we simply put 0. "while with an adjacency list, it may take linear time" - Given that your adjacency list (probably) lacks any natural order, why is it a list instead of a hash set? Adjacency list. . 7. two bits per edge in the optimal representation), and the graph is dense. It is obvious that it requires $O(V^2)$ space regardless of a number of edges. Notes. Is it my fitness level or my single-speed bicycle? Each element of array is a list of corresponding neighbour (or directly connected) vertices.In other words ith list of Adjacency List is a list of all those vertices which is directly connected to ith vertex. Thus, an adjacency list takes up ( V + E) space. This can be done in $O(1)$ time. neighbour ( v 1, v 2): returns true if the vertices v 1 and v 2 are adjacent, and false otherwise. In any case you would inspect all adjacent nodes. 2. When are adjacency lists better than sparse matrices? $$= \log_2 \frac {(N^2)!} Why is the in "posthumous" pronounced as

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