SNADS
Lecture
& Labs
,A graph consists of
Nodes, actors, vertices
Links, ties, edges, relationships, connections
Adjacency Matrix:
• rows and columns represent different nodes
• unweighted
• edges are 0 or 1
• if two nodes are connected, they are said to be adjacent
Edge list
• two-column matrix: sender in first column and receiver in the second column
• In undirected order of the vertices does not matter
Bipartite network
• bimodal network or two-mode network
• two types of nodes, where edges run only between nodes of different types
• incidence matrix (rectangular matrix)
- if n is the number of items or people in the network and g is the number of groups/movies/books/train stations, then the
incidence matrix B is g x n matrix where cell (I,j) is 1 if item j belongs to group I, and 0 otherwise
,Triad closure → when A and B have a connection and A and C have a connection, it is really
likely B and C are going to have a connection
Geodesic → shortest path ( number of edges it goes through )
↳ also called distance
↳ diameter is the longest path
Weighted network → edges are not binary, but have a numeric value ( the number of times a webpage links to another webpage )
Multiplex network → there are multiple kinds of edges possible between nodes
↳ e.g. two people are connected by friendship & coworkership
Degree → measure a node's extroversion, popularity or involvement
Outdegree → number of outgoing edges
Indegree → number of incoming edges
Total degree → total number of neighbours
Closeness → how many steps does it takes to reach all other nodes in the network
↳ sum all the distances from Ito all other vertices
↳ is ill-defined when the network is not fully connected
Stress centrality → measures the amount of stress a vertex has to sustain the network
↳ how many shortest possible routes go through i
Betweenness centrality → Proportion of all shortest paths in the network that pass through i
↳ shows which nodes have information access advantage and are important to the network is efficiency
Centrality → measures how central and individual vertex or edge is within the network
Centralization → measured how centralized the network is as a whole
↳ sum of absolute differences between each centrality and the max centrality (Freeman method)
, You interact more often strongly with who is "near"
Near things are more alike than distant things
y = ρWy + Xβ +
ϵ
Weight matrix
The matrix W captures the social influence process you want to test.
Cell (i, j) captures the weight of the influence that i receives from j.
The weight matrix is usually (but not necessarily) row-normalized so each row adds to 1 exactly.
Mathematically, row or column normalization has the advantages of making the eigenvalues behave nicely, so the likelihood
become nice and smooth.
It also restricts to the interval, making it easy to interpret.
Two views on how people influence each other
Communication Comparison
refers to social influence through the direct contact between Ego compares himself to those alters whom he considers
ego and alter. similar to him in relevant respects, asking himself ‘what
The more frequent and vivid the communication between would that other person do if he were in my shoes?’
ego and alter, the more likely it is that ego will adopt alter’s Ego perceives (or assesses) alter’s behavior and assumes
ideas and beliefs. that behavior to be the ‘correct’ behavior for ‘a-person-like-
Through discussing matters with alter, ego comes to an me’ or for ‘a-person-in-a-position-like-mine
understanding of an issue and adds new information to his
own, which may cause ego to develop similar attitudes and
Operationalising
understandings.
structural equivalence: having precisely the same relations
across all other nodes in the network
Operationalizing
The most straightforward weight matrix is based on the
adjacency matrix: you are influenced by those you are
tied to directly
members of the same component/subgroup
number of two-paths between two people
Lecture
& Labs
,A graph consists of
Nodes, actors, vertices
Links, ties, edges, relationships, connections
Adjacency Matrix:
• rows and columns represent different nodes
• unweighted
• edges are 0 or 1
• if two nodes are connected, they are said to be adjacent
Edge list
• two-column matrix: sender in first column and receiver in the second column
• In undirected order of the vertices does not matter
Bipartite network
• bimodal network or two-mode network
• two types of nodes, where edges run only between nodes of different types
• incidence matrix (rectangular matrix)
- if n is the number of items or people in the network and g is the number of groups/movies/books/train stations, then the
incidence matrix B is g x n matrix where cell (I,j) is 1 if item j belongs to group I, and 0 otherwise
,Triad closure → when A and B have a connection and A and C have a connection, it is really
likely B and C are going to have a connection
Geodesic → shortest path ( number of edges it goes through )
↳ also called distance
↳ diameter is the longest path
Weighted network → edges are not binary, but have a numeric value ( the number of times a webpage links to another webpage )
Multiplex network → there are multiple kinds of edges possible between nodes
↳ e.g. two people are connected by friendship & coworkership
Degree → measure a node's extroversion, popularity or involvement
Outdegree → number of outgoing edges
Indegree → number of incoming edges
Total degree → total number of neighbours
Closeness → how many steps does it takes to reach all other nodes in the network
↳ sum all the distances from Ito all other vertices
↳ is ill-defined when the network is not fully connected
Stress centrality → measures the amount of stress a vertex has to sustain the network
↳ how many shortest possible routes go through i
Betweenness centrality → Proportion of all shortest paths in the network that pass through i
↳ shows which nodes have information access advantage and are important to the network is efficiency
Centrality → measures how central and individual vertex or edge is within the network
Centralization → measured how centralized the network is as a whole
↳ sum of absolute differences between each centrality and the max centrality (Freeman method)
, You interact more often strongly with who is "near"
Near things are more alike than distant things
y = ρWy + Xβ +
ϵ
Weight matrix
The matrix W captures the social influence process you want to test.
Cell (i, j) captures the weight of the influence that i receives from j.
The weight matrix is usually (but not necessarily) row-normalized so each row adds to 1 exactly.
Mathematically, row or column normalization has the advantages of making the eigenvalues behave nicely, so the likelihood
become nice and smooth.
It also restricts to the interval, making it easy to interpret.
Two views on how people influence each other
Communication Comparison
refers to social influence through the direct contact between Ego compares himself to those alters whom he considers
ego and alter. similar to him in relevant respects, asking himself ‘what
The more frequent and vivid the communication between would that other person do if he were in my shoes?’
ego and alter, the more likely it is that ego will adopt alter’s Ego perceives (or assesses) alter’s behavior and assumes
ideas and beliefs. that behavior to be the ‘correct’ behavior for ‘a-person-like-
Through discussing matters with alter, ego comes to an me’ or for ‘a-person-in-a-position-like-mine
understanding of an issue and adds new information to his
own, which may cause ego to develop similar attitudes and
Operationalising
understandings.
structural equivalence: having precisely the same relations
across all other nodes in the network
Operationalizing
The most straightforward weight matrix is based on the
adjacency matrix: you are influenced by those you are
tied to directly
members of the same component/subgroup
number of two-paths between two people
