Network Analysis

../_images/network-analysis.png

Statistical analysis of network data.

Signals

Inputs:

  • Network

    An instance of Network Graph.

  • Items

    Properties of a network file.

Outputs:

  • Network

    An instance of Network Graph with appended information.

  • Items

    New properties of a network file.

Description

Network Analysis widget computes node-level and graph-level summary statistics for the network. It can output a network with the new computed statistics appended or an extended item data table.

Graph level

../_images/network-analysis-graph-level.png
  • Number of nodes: number of vertices in a network.
  • Number of edges: number of connections in a network.
  • Average degree: average number of connections per node.
  • Diameter: maximum eccentricity of the graph.
  • Radius: minimum eccentricity of the graph.
  • Average shortest path length: expected distance between two nodes in the graph.
  • Density: ratio between actual number of edges and maximum number of edges (fully connected graph).
  • Degree assortativity coefficient: correlations between nodes of similar degree.
  • Degree pearson correlation coefficient: same as degree assortativity coefficient but with a scipy.stats.pearsonr function.
  • Estrada index: Estrada index of the graph.
  • Graph clique number: number of nodes in the largest clique (size of a clique).
  • Graph number of cliques: number of cliques (subsets of nodes, where every two nodes are connected).
  • Graph transitivity: ratio of all possible triangles in the network (if node A connects to B and C, how often are B and C connected in the graph).
  • Average clustering coefficient: average of the local clustering coefficients of all the vertices.
  • Number of connected components: number of separate networks in a graph
  • Number of strongly connected components: parts of network where every vertex is reachable from every other vertex (for directed graphs only).
  • Number of weakly connected components: parts of network where replacing all of its directed edges with undirected edges produces a connected (undirected) graph (for directed graphs only).
  • Number of attracting components: node in a direct graph that a random walker in a graph cannot leave (for directed graphs only).

Node level

../_images/network-analysis-node-level.png
  • Degree: number of edges per node.
  • In-degree: number of incoming edges in a directed graph.
  • Out-degree: number of outgoing edges in a directed graph.
  • Average neighbor degree: average degree of neighboring nodes.
  • Clustering coefficient: ratio of triangles in a node neighborhood to all possible triangles.
  • Number of triangles: number of triangles that include a node as one vertex.
  • Squares clustering coefficient: ratio of possible squares that exist for a node.
  • Number of cliques: number of complete (fully connected) subgraphs in a network.
  • Degree centrality: ratio of other nodes connected to the node.
  • In-degree centrality: ratio of incoming edges to a node in a directed graph.
  • Out-degree centrality: ratio of outgoing edges from a node in directed graph.
  • Closeness centrality: distance to all other nodes.
  • Betweenness centrality: measure of control a node exerts over the interaction of other nodes in the network.
  • Information centrality: proportion of total information flow that is controlled by each node.
  • Random-walk betweenness centrality: number of times a node would be on the path between two nodes if employing a random walk.
  • Approx. random-walk betweenness centrality: approximate current-flow betweenness centrality.
  • Eigenvector centrality: score nodes by their connections to high-scoring nodes (measure of centrality of a node based on its connection to other central nodes).
  • Eigenvector centrality (NumPy): eigenvector centrality with NumPy eigenvalue solver.
  • Load centrality: ratio of all shortest paths that lead through the node.
  • Core number: largest value k of a k-core containing that node.
  • Eccentricity: maximum distance between the node and every other node in the network.
  • Closeness vitality: change in the sum of distances for all node pairs when excluding that node.

If Commit automatically is on, new information will be commited automatically. Alternatively, press Commit.

Example

This simple example shows how Network Analysis can enrich the workflow. We have used airtraffic.net as our input network from Network File and sent it to Network Analysis. We’ve decided to compute density, number of cliques and graph transitivity at graph level and degree, clustering coefficient and degree centrality at node level. The widget instantly computes score for graph-level methods and displays them in the widget. It also computes scores for node-level methods, appends them as additional columns and outputs them as Items.

../_images/network-analysis-example.png

We can use node-level scores with Distributions widget to observe, say, clustering coefficient distribution or set the size of nodes in Network Explorer to Degree.