Metrics
GraNa-GraNo provides two different types of metrics: per-graph and per-dependency metrics. All metrics are computed before and after performing normalization and are shown as interactive bar plots that provide the exact result values when hovering on them.
Per-Graph Metrics
We defined five metrics that are computed on a per-graph basis.
| Metric name | Description | Formula |
|---|---|---|
| NodeCount | The number of nodes in a graph \(G\) | \(|N|\) |
| EdgeCount | The number of edges in a graph \(G\) | \(|E|\) |
| AvgNodePropCount | The average number of properties over all nodes | \(\mathsf{avg}\bigl(\bigl\{\bigl|\left\{p\in\mathbf{P}:(n,p) \in \mathsf{dom}(\mathsf{prop})\right\}\bigr|:n\in N\bigr\}\bigr)\) |
| AvgEdgePropCount | The average number of properties over all edges | \(\mathsf{avg}\bigl(\bigl\{\bigl|\left\{p\in\mathbf{P}:(e,p) \in \mathsf{dom}(\mathsf{prop})\right\}\bigr|:e\in E\bigr\}\bigr)\) |
| DisconnectedSubgraphCount | The number of disconnected subgraph in a graph \(G\) |
This per-graph metrics rely on the definition of a labeled property graph as \(G=(N,E,\mathsf{lab},\mathsf{src},\mathsf{tgt},\mathsf{prop}))\), where:
- \(N\) and \(E\) are sets of nodes and edges,
and the functions
- \(\mathsf{lab}\) assigns sets of labels to the nodes and edges
- \(\mathsf{src}\) and \(\mathsf{tgt}\) define the endpoints of the edges
- \(\mathsf{prop}\) assigns constant calues to the property keys in nodes and edges.
Per-Dependency Metrics
For each dependency of the form \(Q :: X \Rightarrow Y\), three metrics are computed:
| Metric name | Description |
|---|---|
| Max- and AvgRedundancyCount | Inspired by Skavantzos et al.1, these two metrics compute the maximum respectively the average of the size of groups of redundant values of the properties in \(X\) and \(Y\). If no redundancies are present, both metrics have a value of 1. |
| Minimality | Based on Ehrlinger et al.2, minimality calculates the ratio between distinct and all pieces of information involving the properties of \(X\) and \(Y\). If all pieces of information are redundant, the value of minimality 0; if all are unique, the value of minimality is 1. |