Overall Graph Metrics

Source: https://www.smrfoundation.org/faq/what-do-all-of-the-overall-graph-metrics-mean/

Vertices

A vertex is an element of a network.

The vertices count is the number of people or things in the network.

Unique Edges

An edge is a connection between two vertices.

The “unique” edges is the number of connections where multiple connections between A and B are counted only once.

Edges With Duplicates

An edge is a connection between two vertices.

The “duplicate” edges count is the total number of multiple connections between two vertices.

Total Edges

An edge is a connection between two vertices.

The “total” edges count is the total number of connections where multiple connections between A and B are all counted.

Self-Loops

An edge that starts and ends in the same vertex is a self loop.

Reciprocated Vertex Pair Ratio

When two vertices both link to each other their connection is “reciprocated”.

This is the percentage of vertices that have a reciprocal relationship.

Reciprocated Edge Ratio

When an edge from A to B is joined by another edge from B to A then their connection is “reciprocated”.

This is the percentage of edges that have a reciprocal relationship.

Connected Components

A group of vertices that are all connected is a component.

This is the number of separate sets of connected vertices.

Single-Vertex Connected Components

A vertex that has zero connections is “isolated” or an “island”.

This is the count of vertices that have zero connections.

Maximum Vertices in a Connected Component

A connected component is composed of a number of vertices.

This is the count of vertices in the largest connected component.

Maximum Edges in a Connected Component

A connected component is composed of a number of edges.

This is the count of total edges in the largest connected component.

Maximum Geodesic Distance (Diameter)

A geodesic is a chain or path composed of edges that link two vertices, potentially through intermediate vertices.

A “shortest path” is the minimum number of connections needed to link two vertices.

The “longest” “shortest path” is the “maximum geodesic distance”.

Average Geodesic Distance

A geodesic is a chain or path composed of edges that link two vertices, potentially through intermediate vertices.

The average length of these paths is the “average geodesic distance”.

Graph Density

Density is the measure of the number edges among a group of vertices over the total possible number if everyone was connected to everyone.

A high graph density means that most people are connected to many others. A low graph density means that most people are not connected to many others.

Modularity

Modularity is a measure of the fitness of the groups that are created in a clustered network.

A group is a set of vertices.

Many group cluster algorithms are intended to find sets of vertices that are strongly connected and relatively separate from other strongly connected groups.

Modularity is the measure of the number of edges that leave a group to connect to vertices in a different group.

If modularity is high, the clusters or groups created may be of low quality. If modularity is low, the groups are well defined.

Modularity ranges between zero, suggesting completely overlapping clusters, and one completely separated clusters. As a rule of thumb, values above .6 are indicative of high level of modularity. Values between .4 and .6 are a moderate level of modularity and values under .4 are low level of modularity. Higher modularity signals that the unique characteristics of clusters are important.