it gives the densities of the subgraphs with diameter n

it gives the eigenvector centralities of the edges

it gives the number of different paths of length n between two nodes

it gives the number of incident paths of nodes of degree n

0-1-2-5

0-3-4-1-2-5

0-1-4-5

0-3-4-5

$$\frac{p_{t-1}\left(3\right)}{\deg\left(3\right)}+\frac{p_{t-1}\left(9\right)}{\deg\left(9\right)}+\frac{p_{t-1}\left(13\right)}{\deg\left(13\right)}$$

$$\frac{1}{size\left(G\right)}$$

$$\frac{1}{order\left(G\right)}$$

$$p_{t-1}\left(8\right)\cdot eccentricity\left(8\right)$$

Dijkstra is a shortest path algorithm, whereas A* is a graph traversal algorithm.

Dijkstra is a DFS based algorithm, and A* is a BFS based algorithm.

Both compute shortest paths, but Dijkstra considers the minimum cost up to the current node, whereas A* adds an heuristic to estimate a lower bound o the future cost.

There are no differences, it is the same algorithm that has different names in Europe and America.

It counts the frequency of the terms in each document.

It down-weights the terms that occur frequently, and increases the weight of ones that occur rarely.

It increases the weight of terms that occur frequently, and down-weights ones that occur rarely.

It merges the terms with the same root, conidering them as synonims in the dictionary.

Cosine

Euclidean

Substraction

Levenshtein

An internet page is ranked in terms of its degree centrality

The relevance of a page is proportional to the probability of being visited by a random walker through the www

An internet page is ranked in terms of its eigenvector centrality

The relevance of a page depends on the relevance of its predecessors

Player 3 because he/she has the highest Page Rank

Players 2 and 6 because they are the ones who throw the most to the basket

Player 1 because he/she has the maximum weighted inbound degree

Player 3 because he/she has the maximum weighted outbound degree

2

3

4

5