Summary Network Society (0HM220)
Lecture 1 Introduction SNA
Network concepts:
- Graph theory: a graph is a set of vertices/nodes/actors and a set of lines/links/edges
between pairs of vertices
o Vertices/node: smallest unit in a graph, e.g. v={1,2,3,4}
o Edges/link, connect two vertices, e.g. E={{1,2}, {1,3}, {2,3}, {3,4}}
o Loop: line that connects a vertex to itself, e.g. email send to yourself
o Directed relationship/arc: X likes Y, X influences Y, in a digraph/directed graph
there are arrows directing at vertices
o Undirected there is no direction of the links
o Simple network: multiple links between vertices or loops are not possible
o Adjacency matrix used to indicate whether persons are connected or not
o Weighted network: links have a weight e.g. number of times persons have
communicated
- Import network data
o Import adjacency data csv file in for of a matrixwe use this, make sure to indicate
the right network, directed/indirected, and weighted/unweighted
o Edgelist, read in list of edges from csv
o Nodelist, for every node, at which it is pointing
- Degree in nondirected graph: the degree of a vertex represents the number of links it has to
other vertices, gives the connectedness
- Degree in a directed graph: indegree (how many are pointing at you), outdegree (number of
points you are pointing at)
- Degree distribution: distribution of all degrees, provides the probability
that a randomly selected vertex in a network has degree k
o For weighted network we use vertex strength: summing up the
weights of edges incident to a given vertex. Again vertex
strength distribution
Centrality: more central means more important/powerful/influential
- Degree centrality: number of connections a node has, and hence the potential access to
resources
- Eigenvector centrality: not only number of connections are important, but how connected
the connections are is taken into account
- Betweenness centrality: how often a certain person is in between the path of others
Social distance: about pairs of actors and connections they have
- Path length: number of links a path contains
- Shortest path/geodesic distance: shortest path to go from one node to another, there can
be multiple geodesic distances (with the same length)
- The longest geodesic distance in network is the diameter
- For a node, the largest geodesic distance is the eccentricity, how far an actor is from the
furthest other
Clustering of social networks:
, - The larger the human network, the lower the density (actual/potential links)
- Component: a subset of nodes in a network, minimum of nodes is 2, every node can
(indirectly) reach each other in a component
- Vertex connectivity: how many nodes do you need to remove to separate the remaining
nodes into two or more components, shows the cohesion of a network. If connectivity>1
there are no articulation points, if it is 1 there are. Articulation points or cut points are the
points that should be removed to separate itis about vulnerability of networks
- Clique: complete subgraphs, everyone is connected to everyone, are very rare
- Community: locally dense connected subgraphs, but not everyone is connected to everyone.
o Modularity: range from -1/2 to +1 (perfect modularity), can be used to find
communities/divisions in a large network
- Density not good to define clustering/cohesion as it depends on the size. We use clustering
coefficient/transitivity index, transitive triad: if a is connected to B, and A is connected to C,
B should also be connected to C. Transitivity measures the probability that the adjacent
vertices of a vertex are connected. The total transitivity is how often there is transitivity, e.g.
3 out of 5 are connected =0.6
Small worlds: found in many real-world phenomena, properties:
1. Networks are very clustered, they are connected via long-distance/weak ties
2. The average path length is rather short
Lecture 2 Social network theories
Three questions about the arguments of classical social network theories:
- What effects do networks have?
- Which network characteristic matter?
- Why do they matter/what is the effect of the characteristics?
Network: a set of ties (relations) amongst a set of actors
Two network characteristics that matter, innovation success benefits from:
- Macro point of view (whole network): network closure facilitates the emergence of trust
and thereby successful collaboration between actors
- Micro point of view (single actor): network diversity important since it provides access to
brokerage benefits, diverse resources, innovative ideas
- There is not one best network configuration, different networks are beneficial in different
situations
o Close-kit networks optimize benefits from collaboration
o Diverse networks optimize competitive benefits
Basic social network arguments/theories:
1. The strength of weak ties (Granovetter):
- We can determine the strength of ties based on the (1) frequency of interaction, (2)
emotional closeness, (3) duration of contact
- More than half found job through personal contacts, many of these contacts were weak ties.
Granovetter’s conjecture: strong ties are usually more willing to help out, but are more likely
Lecture 1 Introduction SNA
Network concepts:
- Graph theory: a graph is a set of vertices/nodes/actors and a set of lines/links/edges
between pairs of vertices
o Vertices/node: smallest unit in a graph, e.g. v={1,2,3,4}
o Edges/link, connect two vertices, e.g. E={{1,2}, {1,3}, {2,3}, {3,4}}
o Loop: line that connects a vertex to itself, e.g. email send to yourself
o Directed relationship/arc: X likes Y, X influences Y, in a digraph/directed graph
there are arrows directing at vertices
o Undirected there is no direction of the links
o Simple network: multiple links between vertices or loops are not possible
o Adjacency matrix used to indicate whether persons are connected or not
o Weighted network: links have a weight e.g. number of times persons have
communicated
- Import network data
o Import adjacency data csv file in for of a matrixwe use this, make sure to indicate
the right network, directed/indirected, and weighted/unweighted
o Edgelist, read in list of edges from csv
o Nodelist, for every node, at which it is pointing
- Degree in nondirected graph: the degree of a vertex represents the number of links it has to
other vertices, gives the connectedness
- Degree in a directed graph: indegree (how many are pointing at you), outdegree (number of
points you are pointing at)
- Degree distribution: distribution of all degrees, provides the probability
that a randomly selected vertex in a network has degree k
o For weighted network we use vertex strength: summing up the
weights of edges incident to a given vertex. Again vertex
strength distribution
Centrality: more central means more important/powerful/influential
- Degree centrality: number of connections a node has, and hence the potential access to
resources
- Eigenvector centrality: not only number of connections are important, but how connected
the connections are is taken into account
- Betweenness centrality: how often a certain person is in between the path of others
Social distance: about pairs of actors and connections they have
- Path length: number of links a path contains
- Shortest path/geodesic distance: shortest path to go from one node to another, there can
be multiple geodesic distances (with the same length)
- The longest geodesic distance in network is the diameter
- For a node, the largest geodesic distance is the eccentricity, how far an actor is from the
furthest other
Clustering of social networks:
, - The larger the human network, the lower the density (actual/potential links)
- Component: a subset of nodes in a network, minimum of nodes is 2, every node can
(indirectly) reach each other in a component
- Vertex connectivity: how many nodes do you need to remove to separate the remaining
nodes into two or more components, shows the cohesion of a network. If connectivity>1
there are no articulation points, if it is 1 there are. Articulation points or cut points are the
points that should be removed to separate itis about vulnerability of networks
- Clique: complete subgraphs, everyone is connected to everyone, are very rare
- Community: locally dense connected subgraphs, but not everyone is connected to everyone.
o Modularity: range from -1/2 to +1 (perfect modularity), can be used to find
communities/divisions in a large network
- Density not good to define clustering/cohesion as it depends on the size. We use clustering
coefficient/transitivity index, transitive triad: if a is connected to B, and A is connected to C,
B should also be connected to C. Transitivity measures the probability that the adjacent
vertices of a vertex are connected. The total transitivity is how often there is transitivity, e.g.
3 out of 5 are connected =0.6
Small worlds: found in many real-world phenomena, properties:
1. Networks are very clustered, they are connected via long-distance/weak ties
2. The average path length is rather short
Lecture 2 Social network theories
Three questions about the arguments of classical social network theories:
- What effects do networks have?
- Which network characteristic matter?
- Why do they matter/what is the effect of the characteristics?
Network: a set of ties (relations) amongst a set of actors
Two network characteristics that matter, innovation success benefits from:
- Macro point of view (whole network): network closure facilitates the emergence of trust
and thereby successful collaboration between actors
- Micro point of view (single actor): network diversity important since it provides access to
brokerage benefits, diverse resources, innovative ideas
- There is not one best network configuration, different networks are beneficial in different
situations
o Close-kit networks optimize benefits from collaboration
o Diverse networks optimize competitive benefits
Basic social network arguments/theories:
1. The strength of weak ties (Granovetter):
- We can determine the strength of ties based on the (1) frequency of interaction, (2)
emotional closeness, (3) duration of contact
- More than half found job through personal contacts, many of these contacts were weak ties.
Granovetter’s conjecture: strong ties are usually more willing to help out, but are more likely
