Table 1 NAP’s supported topological features and their explanation

Number of edges

Shows the number of edges in the network. Moderate network of several thousand connections are very acceptable

Number of nodes

Shows the number of nodes in the network. There is no limitation on the number of nodes

Diameter

Shows the length of the longest geodesic. The diameter is calculated by using a breadth-first search like method. The graph-theoretic or geodesic distance between two points is defined as the length of the shortest path between them

Radius

The eccentricity of a vertex is its shortest path distance from the farthest other node in the graph. The smallest eccentricity in a graph is called its radius. The eccentricity of a vertex is calculated by measuring the shortest distance from (or to) the vertex, to (or from) all vertices in the graph, and taking the maximum

Density

The density of a graph is the ratio of the number of edges and the number of possible edges

Number of edges

Shows the number of edges in the network. If the has more than 10,000 edges it will take into account the first 10,000

Average path length

The average number of steps needed to go from a node to any other

Clustering coefficient

A metric to show if the network has the tendency to form clusters

Modularity

This function calculates how modular is a given division of a graph into subgraphs

Number of self-loops

How many nodes are connected to themselves

Average eccentricity

The eccentricity of a vertex is its shortest path distance from the farthest other node in the graph

Average eigenvector centrality

It is a measure of the influence of a node in a network

Assortativity degree

The assortativity coefficient is positive is similar vertices (based on some external property) tend to connect to each, and negative otherwise

Is directed acyclic graph

It returns True (1) or False (0)

Is directed

It returns True (1) or False (0) depending whether the edges are directed or not

Is bipartite

It returns True (1) or False (0) depending whether the graph is bipartite or not

Is chordal

It returns True (1) or False (0). A graph is chordal (or triangulated) if each of its cycles of four or more nodes has a chord, which is an edge joining two nodes that are not adjacent in the cycle. An equivalent definition is that any chordless cycles have at most three nodes

Average number of neighbors

How many neighbors each node of the network has on average

Centralization betweenness

It is an indicator of a node’s centrality in a network. It is equal to the number of shortest paths from all vertices to all others that pass through that node. Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes

Centralization closeness

It measures the speed with which randomly walking messages reach a vertex from elsewhere in the graph

Centralization degree

It is defined as the number of links incident upon a node

Graph mincut

It calculates the minimum st-cut between two vertices in a graph The minimum st-cut between source and target is the minimum total weight of edges needed to remove to eliminate all paths from source to target

Motifs-3

Use of igraph to searches a graph for motifs of size 3

Motifs-4

Use of igraph to searches a graph for motifs of size 4