Simplest way of measuring centrality is by counting the number of connections a node has. This is called 'degree centrality'.
Another way of measuring centrality is to see how far a node from all other nodes of the graph is is. This measure is called as 'closeness centrality' as it measures the path length between pairs of nodes.
'Betweenness Centrality' is the measure of number of times the node acting as a bridge on the shortest path of any other two nodes. That gives how important each n ode in connecting the whole network.
To complicate the centrality further, we have a measure called 'eigenvector centrality'. Eigenvector considers the influence for the node in the network. This methods considers the power of the nodes the current node is connected. To explain it simply, if I am connected to 500 other people on LinkedIn is different from Barak Obama connecting to 500 of his friends on the LinkedIn. His 500 connections are more influential (probably) than my 500 connections. Google's page rank is a variant of Eigenvector Centrality.
When an external factor is considered for each node and implement eigenvector centrality to consider an external α it is called 'alpha centrality'
When we move the alpha centrality measure from one node to cover multiple radii to include first degree, second degree and so on.. With a factors of β(i) and measure the centrality as a function of influence of varying degrees, it is called beta centrality.