Lecture 1 G.1
Terminology
Graph is a set of vertices (nodes, dots, presenting human actors) and edges(lines, links,
relationships)
Loop: vertex is connected to itself (e.g. send yourself a email) --> don't want them in your network
Arc: directed network link, there is an arrow (e.g. x likes y)
Directed graph/Digraph: the edges have meaning {1,2} means direction 1 to 2
Simple graph: does not contain multiple lines between nodes or loops
Weighted network: connection has a meaning and unique weight, e.g. observe how much people
talk to each other (43 times for one node)
Calculations
Degree: the number of connections a certain node has, sum for non-directed graphs
Vertex strength : weighted sum of the edges, so e.g. 12+52 if a node has a edge with 12 and an edge
with weight 52 (don't care about negative numbers)
Path: set of vertices where every vertice is unique (shortest route). route through the network -->
not visiting somebody twice
Path length: numbers of steps (links) in a path, e.g. 5-6-3-8 --> length 3 (count stripes)
Geodesics: shortest path between two nodes, can be multiple one
Diameter: largest geodesic distance in the network
Kind of networks
250 people in network is the maximum
Strong awareness networks are an essential basis for strong information networks (so knowing who
has which information)
ONA: organizational network analysis
Different relationships:
• Relations that revail rigidity (authority relations
• Collaboration and communication
• Information sharing, potential
• Relations that reveal well-being and support
Measures
• Indegree: number of incoming arrows, e.g. how many people select you for the question
"who is your friend?". How often is a certain node selected as an answer for a question. E.g.
popularity
• Outdegree: number of outgoing arrows, so how many people did a certain select for a
certain question. E.g. agreeableness
• Degree distribution: measures the frequencies of incoming and outcoming arrows. E.g. x-as
representing indegree as 1-20 and y-as representing frequencies
• Reciprocity: if I trust someone, it is likely that that someone trusts me too. Reciprocity can
be measured by the probability that a directed edge is reciprocated (the counterpart)
• if there are 23 mutual relationships → 46 reciprocated edges → 102 (total edges)/46
= 0.45 reciprocity
• More reciprocity = cohesion
• Assymmetric: I am giving you advice but you are not giving me advice (e.g. mentor)
• Symmetric: collaborations in which information/advice is exchanged
• Symmetric friendships are stronger than asymmetric relationship
• Component: path between largest part of nodes of the network
, • Isolates: not connected to a node
• Multiplex relationships: multiple relational dimensions (so multiple components)
• Sparse network: two small components and isolates. Much fewer links than the maximum
possible number of links
Centrality
Centrality: been in centrum of network (often advantageous)
• Degree centrality: number of connections a person has (so higher means more access to
resources)
• Eigenvector centrality: Who you are connected to, so connected to people with higher
degree centrality is better --> bigger nodes means well connectedness
• Betweenness centrality: managers that are in between others (so be between 2 groups).
They are in typical more powerful, cause get most information. How often a certain node is
in within the shortest path between a pair of nodes.
Subgroup analysis
Components
Components; separate groups of a network, an isolated group
Cliques
Cliques: a subgroup where all actors have ties to each-other. It is maximal when no other
actors can be added such that there is a completely connected subgroup
• Line between each node. E.g. 1-2 1-3 and 2-3.
• Cliques may overlap, e.g. a person can be part of multiple cliques. This means this
person has a good position
Dyad: strongest inside a clique, two nodes that are linked
Communities
Community: a set of nodes that has a relatively large number of internal ties. And also
relatively few ties from the group to other parts of the network --> more realistic than cliques
in normal society
Bridges: connect groups (ties between communities), without them it falls apart. So really
important
Characterizing groups/networks
Density: how many links a network has as a ratio of the maximum possible ties. Sow how many are
there possible and how much links are there actually. Density 0 if nobody connected to anybody.
Density 1 if everyone is connected to everyone (clique)
• Downside is that density depends on the size of the network. Larger social networks have
smaller densities --> therefore use average degree.
• Average degree: Degree of every person in the network/number of persons in the
network
• Group degree centralization: how many nodes a person has is a measure for how
central someone is in a group. variation in degree is a measure of inequality
Cluster: locally dense connected subgraph in a network measured by clustering → closure of a triad
Triplet: triangles around a certain node
➔ Look for possibilities and check if this triplet is open or closed (closed =
triangle=triplet)
Local clustering coefficient: the number of possible triangles / connected triplets
Terminology
Graph is a set of vertices (nodes, dots, presenting human actors) and edges(lines, links,
relationships)
Loop: vertex is connected to itself (e.g. send yourself a email) --> don't want them in your network
Arc: directed network link, there is an arrow (e.g. x likes y)
Directed graph/Digraph: the edges have meaning {1,2} means direction 1 to 2
Simple graph: does not contain multiple lines between nodes or loops
Weighted network: connection has a meaning and unique weight, e.g. observe how much people
talk to each other (43 times for one node)
Calculations
Degree: the number of connections a certain node has, sum for non-directed graphs
Vertex strength : weighted sum of the edges, so e.g. 12+52 if a node has a edge with 12 and an edge
with weight 52 (don't care about negative numbers)
Path: set of vertices where every vertice is unique (shortest route). route through the network -->
not visiting somebody twice
Path length: numbers of steps (links) in a path, e.g. 5-6-3-8 --> length 3 (count stripes)
Geodesics: shortest path between two nodes, can be multiple one
Diameter: largest geodesic distance in the network
Kind of networks
250 people in network is the maximum
Strong awareness networks are an essential basis for strong information networks (so knowing who
has which information)
ONA: organizational network analysis
Different relationships:
• Relations that revail rigidity (authority relations
• Collaboration and communication
• Information sharing, potential
• Relations that reveal well-being and support
Measures
• Indegree: number of incoming arrows, e.g. how many people select you for the question
"who is your friend?". How often is a certain node selected as an answer for a question. E.g.
popularity
• Outdegree: number of outgoing arrows, so how many people did a certain select for a
certain question. E.g. agreeableness
• Degree distribution: measures the frequencies of incoming and outcoming arrows. E.g. x-as
representing indegree as 1-20 and y-as representing frequencies
• Reciprocity: if I trust someone, it is likely that that someone trusts me too. Reciprocity can
be measured by the probability that a directed edge is reciprocated (the counterpart)
• if there are 23 mutual relationships → 46 reciprocated edges → 102 (total edges)/46
= 0.45 reciprocity
• More reciprocity = cohesion
• Assymmetric: I am giving you advice but you are not giving me advice (e.g. mentor)
• Symmetric: collaborations in which information/advice is exchanged
• Symmetric friendships are stronger than asymmetric relationship
• Component: path between largest part of nodes of the network
, • Isolates: not connected to a node
• Multiplex relationships: multiple relational dimensions (so multiple components)
• Sparse network: two small components and isolates. Much fewer links than the maximum
possible number of links
Centrality
Centrality: been in centrum of network (often advantageous)
• Degree centrality: number of connections a person has (so higher means more access to
resources)
• Eigenvector centrality: Who you are connected to, so connected to people with higher
degree centrality is better --> bigger nodes means well connectedness
• Betweenness centrality: managers that are in between others (so be between 2 groups).
They are in typical more powerful, cause get most information. How often a certain node is
in within the shortest path between a pair of nodes.
Subgroup analysis
Components
Components; separate groups of a network, an isolated group
Cliques
Cliques: a subgroup where all actors have ties to each-other. It is maximal when no other
actors can be added such that there is a completely connected subgroup
• Line between each node. E.g. 1-2 1-3 and 2-3.
• Cliques may overlap, e.g. a person can be part of multiple cliques. This means this
person has a good position
Dyad: strongest inside a clique, two nodes that are linked
Communities
Community: a set of nodes that has a relatively large number of internal ties. And also
relatively few ties from the group to other parts of the network --> more realistic than cliques
in normal society
Bridges: connect groups (ties between communities), without them it falls apart. So really
important
Characterizing groups/networks
Density: how many links a network has as a ratio of the maximum possible ties. Sow how many are
there possible and how much links are there actually. Density 0 if nobody connected to anybody.
Density 1 if everyone is connected to everyone (clique)
• Downside is that density depends on the size of the network. Larger social networks have
smaller densities --> therefore use average degree.
• Average degree: Degree of every person in the network/number of persons in the
network
• Group degree centralization: how many nodes a person has is a measure for how
central someone is in a group. variation in degree is a measure of inequality
Cluster: locally dense connected subgraph in a network measured by clustering → closure of a triad
Triplet: triangles around a certain node
➔ Look for possibilities and check if this triplet is open or closed (closed =
triangle=triplet)
Local clustering coefficient: the number of possible triangles / connected triplets
