29 Network Cognition and Cognitive Social Structures

Historically, social network analysis (SNA) developed with a strong focus on “objective,” behavioral social relationships—who actually talks to whom, who lends money to whom, or who is related by blood. However, in the late 1980s, network science experienced what can be called the cognitive turn. Led by the sociologist David Krackhardt, researchers began to emphasize that networks are not just external patterns of behavior; they are also mental maps that individuals construct, store, and utilize.

This chapter explores network cognition—how people perceive, represent, and sometimes distort the social structures around them. We focus on David Krackhardt’s seminal Cognitive Social Structures (CSS) framework (Krackhardt 1987), the mathematical methods used to aggregate subjective perceptions into objective structures, and classical empirical studies demonstrating the profound link between cognitive accuracy and organizational power (Krackhardt 1990).

29.1 The Cognitive Turn in Network Science

In everyday life, we do not have an objective, bird’s-eye view of our social networks. Instead, we must rely on our cognitive representations of who is connected to whom. For example, when deciding whether to ask a colleague for a favor, or trying to understand why a promotion went to a rival, we navigate the “informal organizational chart” that exists in our minds.

This cognitive layer of social networks is crucial for three reasons: 1. Action is Guided by Perception: We act based on what we believe the network structure is, not necessarily what it actually is. If $i$ falsely believes that $j$ and $h$ are close friends, $i$ will behave with the caution appropriate for a tight-knit triad, regardless of whether $j$ and $h$ actually dislike each other. 2. Perceptions Vary Widely: Different individuals in the same organization hold wildly different mental maps of the same network. These variations are structured by an individual’s structural position (e.g., central actors have more accurate maps than peripheral ones). 3. Accuracy is a Resource: Having a structurally accurate map of informal relationships is an independent source of power, influence, and strategic advantage.

To measure this mental landscape systematically, Krackhardt (1987) designed a survey and mathematical methodology called Cognitive Social Structures (CSS).

29.3 CSS Aggregations: Reconstructing the “Actual” Network

Because CSS surveys collect $N$ different versions of the network, network analysts face a critical challenge: How do we combine these subjective slices to approximate the “actual” underlying network?

Krackhardt (1987) proposed two primary aggregation approaches: Locally Aggregated Structures (LAS) and Consensus Structures (CS).

Krackhardt, David. 1987. “Cognitive Social Structures.” Social Networks 9 (2): 109–34.

29.3.1 1. Locally Aggregated Structures (LAS)

Locally Aggregated Structures combine the direct perceptions of the two parties directly involved in a given dyad (the sender $i$ and the receiver $j$), ignoring the reports of all other third-party observers. There are two standard ways to define an LAS tie:

29.3.1.1 The Intersection LAS (Agreement LAS)

A directed tie $i \rightarrow j$ is considered to exist only if both $i$ and $j$ agree that $i$ sends a tie to $j$. That is, the sender reports sending it, and the receiver reports receiving it:

\[ LAS^{\cap}_{ij} = R_{iji} \times R_{ijj} \tag{29.3}\]

This is a highly conservative measure of a tie, representing strong mutual agreement.

29.3.1.2 The Union LAS (Or LAS)

A directed tie $i \rightarrow j$ is considered to exist if either $i$ or $j$ (or both) report that a tie exists from $i$ to $j$:

\[ LAS^{\cup}_{ij} = \max(R_{iji}, R_{ijj}) \tag{29.4}\]

This is a more inclusive measure, capturing any relation that has at least some behavioral or perceived foundation from either of the primary actors.

29.3.2 2. Consensus Structures (CS)

Sometimes, we want to leverage the “wisdom of the crowd.” A Consensus Structure aggregates the perceptions of the entire group (or a subset of disinterested third-party observers) to determine whether a tie is “real.”

29.3.2.1 Threshold Consensus ($\alpha$)

Under a threshold consensus model, a tie $i \rightarrow j$ is considered to exist if at least a certain proportion $\alpha$ of all group members perceive it:

\[ CS^{\alpha}_{ij} = 1 \quad \text{if} \quad \frac{\sum_{k} R_{ijk}}{N} \ge \alpha, \quad \text{else} \quad 0 \tag{29.5}\]

Where $N$ is the number of perceivers.

Majority Consensus ($\alpha = 0.50$): A tie is considered active if more than $50\%$ of the organization’s members agree that it exists.
Stricter Consensus ($\alpha = 0.75$): A tie is considered active only if a solid three-quarters majority of the group agrees on its existence.

Table Table 29.1 contrasts these three classical aggregation methods:

Table 29.1: CSS Aggregation and Reconstructions

Aggregation Method	Mathematical Definition	Sociological Focus	Key Property
Intersection LAS ($LAS^{\cap}$)	$R_{iji} \times R_{ijj} = 1$	Mutual agreement and dyadic confirmation.	High reliability; low density.
Union LAS ($LAS^{\cup}$)	$\max(R_{iji}, R_{ijj}) = 1$	Inclusivity; capturing any active connection.	Low barrier; high density.
Consensus Structure ($CS^{0.50}$)	$\frac{\sum_k R_{ijk}}{N} \ge 0.50$	Public recognition and organizational reputation.	Filters out individual noise/bias.

29.4 Measuring Cognitive Accuracy

Once we have reconstructed a consensus or behavioral network (such as the majority consensus structure $\mathbf{CS}$), we can compare each individual’s subjective slice ($\mathbf{R}_{..k}$) to this standard to measure their cognitive accuracy.

29.4.1 1. Structural Accuracy (Hamming Distance)

The simplest way to calculate accuracy is by computing the Hamming distance between person $k$’s cognitive slice and the consensus matrix. The Hamming distance is the count of cells where the individual’s perception disagrees with the consensus:

\[ \text{Hamming Distance}(k) = \sum_{i,j} |R_{ijk} - CS_{ij}| \tag{29.6}\]

A lower Hamming distance represents higher accuracy (fewer perceptual errors).

29.4.2 2. Relational Accuracy (QAP Correlation)

Because social networks are structurally interdependent (violating standard statistical assumptions of independence), researchers typically compute the correlation between the vectorized matrices $\mathbf{R}_{..k}$ and $\mathbf{CS}$ using the Quadratic Assignment Procedure (QAP). A higher QAP correlation coefficient ($r \in [-1.0, +1.0]$) represents a more structurally accurate mental map of the organization.

29.4.3 Cognitive Network Biases

Human brains are not perfect recorders; they are wired to simplify complex information. When individuals reconstruct networks in their minds, they systematically introduce three cognitive biases:

Ego Bias (Centrality Inflation): Individuals consistently overestimate their own popularity, centrality, and closeness to prestigious others. Egos routinely perceive themselves as receiving more incoming ties (indegree) than the consensus structure supports.
Reciprocity Bias (Symmetry Pressure): Humans experience cognitive discomfort with unreciprocated friendships. Consequently, if person $i$ nominates $j$ as a friend, $i$’s mental slice $\mathbf{R}_{..i}$ will almost always depict $j$ reciprocating that friendship ($R_{jii} = 1$), even if $j$’s actual report is null.
Balance Bias (Transitivity Pressure): Drawing from Heider’s balance theory (see Chapter 42), our minds prefer closed, balanced triads. If $i$ knows that $j$ and $h$ are their friends, $i’s brain will mentally “close” the triangle, perceiving $j$ and $h$ to be friends ($R_{jhi} = 1$) even if they have no connection.

29.5 Applied Research: Structure, Cognition, and Power

Does having a more accurate mental map of your social network make you more powerful? This fundamental question was tested in David Krackhardt’s landmark 1990 study, “Assessing the Political Landscape: Structure, Cognition, and Power in Organizations” (Krackhardt 1990).

Krackhardt, David. 1990. “Assessing the Political Landscape: Structure, Cognition, and Power in Organizations.” Administrative Science Quarterly 35 (2): 342–69.

29.5.1 The Silicon Systems Study

Krackhardt surveyed a small manufacturing firm of $N = 36$ employees, including managers and supervisors (the “Silicon Systems” company). He collected complete CSS data for two distinct networks: 1. The Advice Network: Who goes to whom for work-related technical help or advice. 2. The Friendship Network: Who hangs out with whom outside of formal work duties.

He also measured Reputed Power by asking every employee to rate the relative power and influence of every other employee in the organization on a 1-to-5 scale.

29.5.2 Key Findings and Results

Krackhardt calculated the cognitive accuracy of each of the 36 employees’ mental slices against the consensus network. He then ran multiple regressions to predict reputed power:

Accuracy is Power: An individual’s cognitive accuracy regarding the advice network was highly and positively associated with their reputed power within the firm ($r = 0.51$, $p < 0.001$).
The Advice Advantage: Interestingly, accuracy regarding the advice network was far more critical for power than accuracy regarding the friendship network. Power was tied to knowing who holds technical expertise and institutional knowledge, rather than knowing who hangs out with whom.
Centrality Control: Most importantly, this effect remained highly significant even when controlling for actual network centrality (such as actual advice indegree or betweenness).

\[\text{Advice Accuracy} \implies \text{Power} \quad (\text{Independent of actual Centrality})\]

29.5.3 Why is Perceptual Accuracy an Independent Source of Power?

An employee who holds an accurate “cognitive map” of the advice network has a decisive strategic advantage. They know: * Who actually influences whom (allowing them to lobby key influencers rather than formal figureheads). * Where the actual structural holes and bottlenecks lie (allowing them to position themselves as brokers, see Chapter 38). * Who is dependent on whom (allowing them to predict coalition-building and political dynamics).

Conversely, highly central actors who have inaccurate mental maps are “structurally blind.” They are prone to political missteps, making coalitions with marginal actors or misjudging the influence of key gatekeepers.

29.6 Applied Research: Simmelian Ties and Constraint

Krackhardt’s work bridging cognition and structure also led to the development of Simmelian Tie Theory (1999).

Named after the classical German sociologist Georg Simmel, a Simmelian tie is a highly constrained, strong tie. Two actors, $i$ and $j$, share a Simmelian tie if: 1. They have a mutually reciprocated tie ($i \leftrightarrow j$). 2. They are both mutually connected to a third party $h$ ($i \leftrightarrow h$ and $j \leftrightarrow h$), forming a mutual clique of size three or larger.

29.6.1 The “Torture” of Simmelian Cliues

Krackhardt (1999) famously referred to Simmelian ties as “the ties that torture.”

Krackhardt, David. 1999. “The Ties That Torture: Simmelian Tie Analysis in Organizations.” Research in the Sociology of Organizations 16 (1): 183–210.

Unlike a simple, unconstrained dyadic tie where two individuals can negotiate their relationship bilaterally, a Simmelian tie is heavily monitored and constrained by third-party observers. In a Simmelian clique: * Expectations of Conformity: The group demands high consensus. Individual deviance is immediately observed, sanctioned, and corrected by the other members. * Reduced Autonomy: Individuals experience high cognitive and behavioral “torture” because they must subordinate their personal opinions and bilateral negotiations to preserve the stability and consensus of the triad.

While weak ties provide access to novel information (see Chapter 37), Simmelian ties represent the ultimate structural constraint, locking individuals into stable, norm-enforced communities that resist change but provide extreme trust and stability.