Global structures and local network mechanisms of knowledge-flow networks

Understanding the patterns and underlying mechanisms that come into play when employees exchange their knowledge is crucial for their work performance and professional development. Although much is known about the relationship between certain global network properties of knowledge-flow networks and work performance, less is known about the emergence of specific global network structures of knowledge flow. The paper therefore aims to identify a global network structure in blockmodel terms within an empirical knowledge-flow network and discuss whether the selected local network mechanisms are able to drive the network towards the chosen global network structure. Existing studies of knowledge-flow networks are relied on to determine the local network mechanisms. Agent-based modelling shows the selected local network mechanisms are able to drive the network towards the assumed hierarchical global structure.

mechanisms, the network statistics are calculated and weighted by . The weighted network statistics are normalized on the interval between zero and one. Among 25% of the units with the highest weighted network statistics value, one unit is randomly selected.
Further, the tenure is calculated at each iteration and the new units (newcomers, see section 1.3 in this appendix) are added to the network and some existing units are removed (outgoers, see section 1.4 in this appendix) at the selected iterations.

Weighted network statistics
The weighted network statistics are calculated by the function . ( , , , ) that considers the set of mechanisms and the weights of the corresponding mechanisms . is a set of operationalized mechanisms defined on the binarized network and unit .
The computed value of a given mechanism (from the set of mechanisms ) is a vector of length .
Each element of such vector corresponds to one unit in the network. When several mechanisms are considered, the vectors can be organized into matrix with rows and columns representing the mechanisms. The matrix so obtained is weighted as = resulting in a vector of length which is returned by the function . ( , , , ).
1 The probabilities could be different among the units. For example, it could be assumed that those units with a lower tenure will have more opportunities to ask for advice. However, whether this would be a reasonable assumption it depends on the company's policies and organizational culture. To consider the most parsimonious case, it is assumed, in this study, that all the units have equal probabilities to ask for advice at any time.

Duration of the links
No specific mechanism considered in this study would control the duration of a link (i.e. duration of the advice seeker-advice giver interaction). Instead, it is assumed that all interactions last the same amount of time. One unit of time is defined through the number of iterations at which each unit will receive (on average) the selected number ( ) of opportunities to establish a link. The number of iterations depends on the network's size and the desired maximum expected out-degree (parameter ).
Let us consider a case without newcomers and outgoers. Further, let us assume there are units in the network and each unit has up to opportunities to establish (or confirm) a link (the loops are not considered). On the assumption that the units are chosen randomly with equal probability, the number of iterations needed to reach the expected number of opportunities to establish a link is = (namely, the length of one unit of time In order to ensure enough iterations so that the considered mechanisms can affect a global network structure considerably, the number of iterations is multiplied by the constant . The value of > 1 increases the expected number of opportunities for each unit to establish a link while it does not affect the duration of a link and the maximal expected out-degree. A higher expected number of opportunities for each unit to create a tie can also increases the structure's stabilization before the new units are added. In other words, a higher number of iterations gives "more time" to the mechanisms to affect the global network structure before the newcomers are added to the network.

Newcomers
New units can be added one by one or in several waves. The iterations upon which the new units are added to the network can be selected in different ways: (i) one unit can be added at a time; or (ii) a group of units can be added all at once. Further, the unit (or groups of units) can be added at randomly selected iterations or be added at predefined iterations e.g., equally distributed across the iterations. In this study, newcomers are added in three waves. The number of newcomers for each wave is represented by vector ℵ. The number of iterations between each wave is determined based on the total number of units in the network, based on parameter and parameter .

Outgoers
The number of outgoers can be selected arbitrarily. They can leave the network in waves just before or after newcomers are added or can leave the network one by one. With this implementation of the algorithm, the outgoers leave the network at the selected iterations in vector . The units to be removed from the network can be selected based on their personal characteristics (e.g., tenure), network characteristics (e.g., popularity or hierarchical level), or randomly. Here, the units to be removed are randomly selected, which is in line with the observations on the empirical data. The number of units to be removed from the network is 25% of all units in the network calculated immediately after a wave of newcomers has been added to the network.
Algorithm 1 The algorithm for generating networks import initial network (a matrix with rows and columns, where is the number of units) import (a vector with the mechanisms' weights) import (a set of functions which defines the mechanisms) set (the expected maximum out-degree) set (the factor by which the number of iterations must be increased between the waves) set ℵ (a vector with the number of newcomers per waves) set (a vector with iterations at which the outgoings are to be removed) set (tenure, a vector of length ) compute = cumsum ( |__| if ≥ 3 ( ) then classify a corresponding unit into set (where 3 is the third quartile) |__| randomly select unit among the units from set |__| set a link → |__| calculate = − 1 ( + 1) ⁄ |__| calculate = { 0, ≤ 0 , > 0 | if ∈ |________|randomly select a unit or a group of units to be removed |________|remove the selected unit(s) and update X and T accordingly |if ∈ and ≠ : |________|add a unit or a group of units and update and accordingly |________|set to next element of return network