Basic Network Terminology  Vertex  A vertex is simply drawn as a node or a dot.
 Edge  An edge (a set of two elements) is drawn as a line
connecting two vertices, called endpoints or end vertices or end vertices.
 Directed Edge  A directed edge is an ordered pair of nodes that can be represented graphically as an arrow drawn between the nodes.
 Undirected Edge  An undirected edge disregards any sense of direction and treats both nodes interchangeably.
 Node Degree  The degree of a node in a network is the number of
connections it has to other nodes and the degree distribution is the
probability distribution of these degrees over the whole network.
 Out Degree  The number of edges leaving a vertex.
 In Degree  The number of edges entering a vertex.
 Size  The size of a graph is the number of its edges.
 Weight  A weighted graph associates a label (weight) with every edge in the graph. Weights are usually real numbers. The weight of an edge is often referred to as the "cost" of the edge. In applications, the weight may be a measure of the length of a route, the capacity of a line, the energy required to move between locations along a route, etc.
Network Overview  Average Degree  Average number of links per node.
 Average Weighted Degree  Average of sum of weights of the edges of nodes.
 Distance  The distance between two nodes is defined as the number of
edges along the shortest path connecting them.
 Average Distance  The Average of distance between all pairs of nodes.
 Network Diameter  The maximum distance between any pair of nodes in the graph.
 Modularity  Modularity is one measure of the structure of networks or
graphs. It was designed to measure the strength of division of a network into
modules (also called groups, clusters or communities). Networks with high
modularity have dense connections between the nodes within modules but sparse
connections between nodes in different modules.
 Connected Components  a connected component (or just component) of an undirected
graph is a subgraph in which any two vertices are connected to each other by
paths, and which is connected to no additional vertices in the supergraph.
Node Overview  Clustering Coefficient  a clustering coefficient is a measure of the degree to which
nodes in a graph tend to cluster together.
 Centrality  centrality refers to indicators which identify the most
important vertices within a graph. Applications include identifying the most
influential person(s) in a social network, key infrastructure nodes in the
Internet or urban networks, and super spreaders of disease.
 Closeness Centrality  In connected graphs there is a natural distance metric
between all pairs of nodes, defined by the length of their shortest paths. The
farness of a node is defined as the sum of its distances to all other nodes,
and its closeness is defined as the reciprocal of the farness. Thus, the more
central a node is the lower its total distance to all other nodes.
 Betweenness Centrality  Betweenness is a centrality measure of a vertex within a
graph (there is also edge betweenness, which is not discussed here). Betweenness
centrality quantifies the number of times a node acts as a bridge along the
shortest path between two other nodes.
 Eigenvector Centrality  Eigenvector centrality is a measure of the influence of a
node in a network. It assigns relative scores to all nodes in the network based
on the concept that connections to highscoring nodes contribute more to the
score of the node in question than equal connections to lowscoring nodes.
Edge Overview  Average Path Length  Average path length is defined as the average number of steps along the shortest paths for all possible pairs of network nodes. It is a measure of the efficiency of information or mass transport on a network.

