An independent study reference written by Dr Phuc V. Nguyen. It is not official subject material — for assessment requirements always follow your subject outline and vUWS.

Networksbeginner

Actors and ties

Q: A team maps "who reviews whose code" and then treats the network as undirected to simplify the analysis. What is the main cost of that choice?

Reviewing and being reviewed collapse into one score, hiding who carries the review load. Symmetrising throws away the arrow. Someone who reviews 12 colleagues and someone reviewed by 12 colleagues both end up with a degree of 12, even though one is a bottleneck of effort and the other is a junior being supervised. Density and drawing still work. What is lost is meaning.

Q: An analyst builds an employee network by connecting anyone who attended the same all-staff meeting. Density comes out close to one. The most likely reading is that

the projection from event attendance created ties that match no real relation. A single event attended by everyone projects into a complete graph, because every attendee is joined to every other. The density is an artefact of the projection rule, not evidence about behaviour. Two-mode data needs either a weighting by the number of shared events or a relation closer to actual interaction.

A network is a set of actors and a set of ties between them. Actors, also called nodes, are whatever the study treats as a unit: people, teams, firms, accounts, products, documents. Ties, also called edges, are the one specific relation being measured. A tie can be undirected, where the connection has no natural direction such as sitting on the same committee, or directed, where it runs one way such as asks advice of, or pays. Whatever the picture looks like, the network can be represented as an adjacency matrix with one row and one column per actor, and equally as an edge list, or as an incidence matrix when actors are joined to events rather than to each other.

Why it matters

A network is a seating chart plus a list of who passes notes to whom. The seating chart is the actors. The notes are the ties. If notes travel both ways you can draw a plain line. If they only go one way you need an arrow, because being asked for advice by ten people is a completely different position from asking ten people for advice.

Before you read on — recall

A team maps "who reviews whose code" and then treats the network as undirected to simplify the analysis. What is the main cost of that choice?

Formulas

Adjacency matrix entry

a_{ij} = \begin{cases} 1 & \text{if a tie runs from } i \text{ to } j \\ 0 & \text{otherwise} \end{cases}

Every network reduces to this table. If the relation is undirected then

a_{ij} = a_{ji}

and the matrix is symmetric. If it is directed the matrix need not be, and the gap between

a_{ij}

and

a_{ji}

is exactly the information an arrow carries.

Reciprocity of a directed network

r = \frac{\text{pairs tied in both directions}}{\text{pairs tied in at least one direction}}

This is the dyad-based convention, counting mutual pairs against pairs tied at all. An arc-based version instead divides reciprocated arcs by all arcs and returns a different number, so name the one you used. A value near one means the relation is mutual in practice. Advice networks usually score low, because juniors name seniors and seniors do not name back. A low value is a finding about the relation, not a data error.

Worked examples

Scenario

A six-person analytics team is mapped on the relation "goes to this person for help with a work problem at least once every seven days". Ana names Ben, Cara and Dan. Ben names Ana and Cara. Cara names Ana and Ben. Dan names Ana and Eve. Eve names Dan and Finn. Finn names Eve.

Solution

Every pair here is named by both sides, so the relation can be treated as undirected and the matrix is symmetric. Reading across Ana, Ben, Cara, Dan, Eve, Finn, the Ana row is 0, 1, 1, 1, 0, 0 and the Finn row is 0, 0, 0, 0, 1, 0. Six ties in total: Ana-Ben, Ana-Cara, Ana-Dan, Ben-Cara, Dan-Eve, Eve-Finn. This six-tie structure is the running example used by the centrality and density nodes in this cluster.

Scenario

A marketing team has a list of which of its 40 staff attended which of 12 client workshops. There are no person-to-person ties in the data at all.

Solution

This is a two-mode or affiliation network, with two kinds of actor and ties running only between the kinds. It can be projected into a one-mode network by joining two people whenever they attended the same workshop. The projection is useful and it also invents ties, because sharing a room is not the same as speaking. Always report which projection rule was used. A dense-looking co-attendance network often reflects nothing more than a few large events.

Common mistakes

✗An actor has to be a person. An actor is whatever the research question makes the unit. Studies routinely use firms, subsidiaries, bank accounts, products, hashtags or job roles as nodes, and the arithmetic is identical.
✗A tie means the two actors like each other. A tie is only the relation you defined and measured. It might be sends payments to, cites, competes with, or is often confused with. Some of the most useful business networks record dependency or conflict, not affinity.
✗Direction is a technical detail. Direction changes the meaning of every measure built on it. In an advice network, ties received read as being relied upon and ties sent read as seeking help. Treating the network as undirected merges the two into a number that means neither.
✗A network is not really structured data because it is a picture. A network is structured data of a particular shape, a set of relations that can be held as a square matrix or as an edge list, and it is stored, joined and validated like any other table.

Revision bullets

•Actors are nodes, ties are edges, and both are defined by the research question
•Undirected ties are symmetric; directed ties carry an arrow and a meaning
•The adjacency matrix entry a_ij is one common representation; an edge list holds the same relation
•Reciprocity measures how often a directed tie is returned
•Two-mode data joins actors to events; projecting it to one mode invents ties

Quick check

A team maps "who reviews whose code" and then treats the network as undirected to simplify the analysis. What is the main cost of that choice?

An analyst builds an employee network by connecting anyone who attended the same all-staff meeting. Density comes out close to one. The most likely reading is that

Connected topics

Forms of Data What SNA Is Weighted Ties Degree Centrality Density Network Study

More in Networks

Closeness Betweenness Bridges and Cliques

Sources

Borgatti et al. (2009)
Borgatti, S. P., Mehra, A., Brass, D. J., & Labianca, G. "Network Analysis in the Social Sciences." Science, 323(5916), 892-895, 2009.
Sorts ties into similarities, social relations, interactions and flows, which is a useful check before defining a relation.
Wasserman & Faust (1994), Chs 3-4
Wasserman, S., & Faust, K. Social Network Analysis: Methods and Applications. Cambridge University Press, 1994.
Formal treatment of adjacency matrices, directed relations and two-mode affiliation data.

How to cite this page

Dr. Phil's Quant Lab. (2026). Actors and ties. Derivatives Atlas. https://phucnguyenvan.com/concept/ba-actors-ties