17. Analyzer¶
Analyzer computes a comprehensive set of topological metrics for undirected and directed networks, including:
Number of nodes, edges and connected components.
Network diameter, radius and clustering coefficient, as well as the characteristic path length.
Charts for topological coefficients, betweenness, and closeness.
Distributions of degrees, neighborhood connectiveness, average clustering coefficients, shortest path lengths, number of shared neighbors and stress centrality.
17.1. Network Analysis¶
Analyze Network¶
To run Analyzer, select Tools → Analyze Network.
Analyzer will run different statistics depending on whether the network is directed or undirected, with the default being undirected. A Set Parameters dialog will open where you can specify if the network should be analyzed as a directed graph.
When results are ready, they will appear in the Results Panel.
The header of the Results Panel shows the interpretation used (Directed or Undirected) and the name of the analyzed network, next to a New Analysis… button that runs the analysis again — for example, under the other interpretation.
The Summary Statistics table lists the network-level metrics described below. Hover over a row for a short explanation of that metric, or select a row to see a longer description — including its formula, where there is one — in the area below the table. The copy button next to the table title copies all statistics to the clipboard. Node-specific statistics are added to the Node Table, and edge Betweenness to the Edge Table.
The bottom of the panel has buttons that chart the node degree distribution and betweenness by degree; for a directed analysis, radio buttons select whether Indegree or Outdegree is plotted.
Summary Statistics¶
The metrics below appear in the Summary Statistics table, in this order. All of them are computed by both interpretations unless marked otherwise.
Number of nodes
The total number of nodes in the network, including nodes with no connections.
Number of edges
The total number of edges in the network, as interpreted by the analysis (paired edges may have been combined, depending on the chosen interpretation).
Avg. number of neighbors
The average number of neighbors over all nodes, indicating the average connectivity of a node in the network. For a simple undirected network, the network density equals this value divided by (N - 1), where N is the number of nodes. In a directed analysis, neighbors are counted regardless of edge direction.
Network diameter
The distance between two nodes is the length, in edges, of the shortest path between them. The network diameter is the largest distance between any two nodes; node pairs with no connecting path are ignored. In a directed analysis, paths follow edge direction.
Network radius
The eccentricity of a node is the largest shortest-path distance from that node to any other node in its connected component. The network radius is the smallest non-zero node eccentricity (the diameter is the largest). In a directed analysis, the eccentricity of a node is the largest shortest-path distance from it to any node reachable from it, following edge direction.
Characteristic path length
Also known as the average shortest path length: the average shortest-path distance over all node pairs for which a path exists. It gives the expected distance between two randomly chosen connected nodes. In a directed analysis, paths follow edge direction and the pairs are ordered: the distance from one node to another may differ from the distance in the opposite direction.
Clustering coefficient
The clustering coefficient of a node n measures how connected its neighbors are to one another: Cn = 2en / (kn(kn - 1)), where kn is the number of neighbors of n and en is the number of edges between those neighbors. The network clustering coefficient is the average of Cn over all nodes, with nodes having fewer than two neighbors counted as 0. It ranges from 0 (no neighbor of any node connects to another neighbor) to 1 (every neighborhood is fully connected).
In a directed analysis, Cn = en / (kn(kn - 1)), where kn is the number of neighbors of n, counted regardless of edge direction, and en is the number of directed edges between those neighbors, counted individually.
Network density
The fraction of possible edges that actually exist: D = 2E / (N(N - 1)) for a network with N nodes and E edges. It ranges from 0 (no edges) to 1 (every possible edge is present); self-loops and duplicated edges are not considered.
In a directed analysis, D = E / (N(N - 1)), since each pair of nodes may be connected by an edge in each direction.
Network heterogeneity
Undirected analysis only.
The coefficient of variation of the node degrees: the standard deviation of the degrees divided by their mean. A high value indicates greater variation in connectivity and a stronger tendency for some nodes to act as hubs.
Network centralization
Undirected analysis only.
An index of how strongly degree is concentrated in a few nodes: C = (N / (N - 2)) · (kmax / (N - 1) - D), where kmax is the maximum node degree and D is the network density. Star-like networks have centralization close to 1, whereas networks where every node has the same number of neighbors have centralization close to 0.
Connected components
A connected component is a maximal set of nodes such that every pair of nodes is connected by a path within the component. The number of connected components indicates how fragmented the network is: a fully connected network has a single component. Components are always computed ignoring edge direction; for a directed network these are, in graph-theory terms, the weakly connected components.
Multi-edge node pairs
The number of unordered pairs of nodes that are connected by more than one edge (duplicated or parallel edges). Edge direction is ignored, so two edges in opposite directions between the same two nodes also form a multi-edge pair.
Number of self-loops
The number of edges whose source and target are the same node.
Analyze Subset of Nodes¶
Prior versions of this tool offered the option of analyzing all nodes or only a selected subset. This is no longer supported directly in the program. Instead, if you want to analyze a subnetwork, you can use the command File → New Network → From Selected Nodes, All Edges in the Command Panel to create the desired subnetwork.
Plot Metrics¶
Once the Analyzer is run, several additional columns are added to the Node Table (and an EdgeBetweenness column is added to the Edge Table). To plot any of these new columns, right-click on the column header and select Plot Histogram… for a single parameter distribution, or Plot Scatter… for a bivariate plot of the data. Within either of these charts it is possible to select a section of the data, and select the nodes (edges) in the main graph window corresponding to the region selected on the chart.
For additional information about NetworkAnalyzer see Yassen Assenov, Nadezhda Doncheva, Thomas Lengauer, and Mario Albrecht, DOI: 10.1038/nprot.2012.004.