Eigenvector Centrality

First off, we will estimate the cost of running the algorithm using the estimate procedure. This can be done with any execution mode. We will use the write mode in this example. Estimating the algorithm is useful to understand the memory impact that running the algorithm on your graph will have. When you later actually run the algorithm in one of the execution modes the system will perform an estimation. If the estimation shows that there is a very high probability of the execution going over its memory limitations, the execution is prohibited. To read more about this, see Automatic estimation and execution blocking.

For more details on estimate in general, see Memory Estimation.

In the stream execution mode, the algorithm returns the score for each node. This allows us to inspect the results directly or post-process them in Cypher without any side effects. For example, we can order the results to find the nodes with the highest Eigenvector score.

For more details on the stream mode in general, see Stream.

The above query is running the algorithm in stream mode as unweighted. Below, one can find an example for weighted graphs.

In the stats execution mode, the algorithm returns a single row containing a summary of the algorithm result. For example Eigenvector stats returns centrality histogram which can be used to monitor the distribution of centrality scores across all computed nodes. This execution mode does not have any side effects. It can be useful for evaluating algorithm performance by inspecting the computeMillis return item. In the examples below we will omit returning the timings. The full signature of the procedure can be found in the syntax section.

For more details on the stats mode in general, see Stats.

The mutate execution mode extends the stats mode with an important side effect: updating the named graph with a new node property containing the score for that node. The name of the new property is specified using the mandatory configuration parameter mutateProperty. The result is a single summary row, similar to stats, but with some additional metrics. The mutate mode is especially useful when multiple algorithms are used in conjunction.

For more details on the mutate mode in general, see Mutate.

The write execution mode extends the stats mode with an important side effect: writing the score for each node as a property to the Neo4j database. The name of the new property is specified using the mandatory configuration parameter writeProperty. The result is a single summary row, similar to stats, but with some additional metrics. The write mode enables directly persisting the results to the database.

For more details on the write mode in general, see Write.

By default, the algorithm considers the relationships of the graph to be unweighted. To change this behaviour, we can use the relationshipWeightProperty configuration parameter. If the parameter is set, the associated property value is used as relationship weight. In the weighted case, the previous score of a node sent to its neighbors is multiplied by the normalized relationship weight. Note, that negative relationship weights are ignored during the computation.

In the following example, we use the weight property of the input graph as relationship weight property.

As in the unweighted example, the "Home" node has the highest score. In contrast, the "Product" now has the second highest instead of the fourth highest score.

The tolerance configuration parameter denotes the minimum change in scores between iterations. If all scores change less than the configured tolerance, the iteration is aborted and considered converged. Note, that setting a higher tolerance leads to earlier convergence, but also to less accurate centrality scores.

We are using tolerance: 0.1, which leads to slightly different results compared to the stream example. However, the computation converges after three iterations, and we can already observe a trend in the resulting scores.

Personalized Eigenvector Centrality is a variation of Eigenvector Centrality which is biased towards a set of sourceNodes. By default, the power iteration starts with the same value for all nodes: 1 / |V|. For a given set of source nodes S, the initial value of each source node is set to 1 / |S| and to 0 for all remaining nodes.

The following examples show how to run Eigenvector centrality centered around 'Site A'.

Internally, centrality scores are scaled after each iteration using L2 normalization. As a consequence, the final values are already normalized. This behavior cannot be changed as it is part of the power iteration method.

However, to normalize the final scores as part of the algorithm execution, one can use the scaler configuration parameter. A description of all available scalers can be found in the documentation for the scaleProperties procedure.

Comparing the results with the stream example, we can see that the relative order of scores is the same.