Abstract
In order to enable the management of the large presence of similar groups of agents, namely masks, resulting from the implementation of the Relevance Index (RI) algorithm, the ‘PoSH-CADDy’ three-step methodology is here proposed. The developed procedure is based on (i) several rounds of analysis to be performed over reducing sets of agents (with a Progressive Skimming procedure), (ii) the consideration of the overlaps among masks emerging from the output of each round (by means of a Hierachical Cluster Analysis), (iii) a final analysis of the masks remaining from the previous steps (by considering those with a minimum Degree of Dissimilarity). The methodology is implemented in a real socio-economic complex network. Insights from a first explorative analysis are provided.
The views expressed are purely those of the author and may not in any circumstances be regarded as stating an official position of the European Commission.
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Notes
- 1.
There are cases in which, even if any new relationship is established, flickering interactions occur: people daily exchange messages with long-time friends, and enterprises repeatedly collaborate with partners they already know.
- 2.
In the present work, the concepts of (i) masks, (ii) groups, (iii) communities, or (iv) meso-structures, are all treated indistinctly since they all refer to subset of agents belonging to the same system.
- 3.
Not necessarily all agents belong to at least one masks/subset.
- 4.
A homogeneous system is a system having the same number of agents of the system to which it is referred; each agent has a random generated behavior in accordance with the probability of the states it assumes in the reference system.
- 5.
The fact that the number of masks detected does not change, is just a choice of the researcher. This parameter could change but, since this work is not aimed at considering the increasing of the value of M, which has been fixed equal to 15.000 in each round of analysis, M is taken for given. Because of that, M will not be indexed with the number of the round r.
- 6.
Since the initial round that is performed is \(r=1\), if \(r=1 \rightarrow q=0\). As there is no round 0, if \(q=0 \rightarrow B_{0}^{1}=\varnothing \). Therefore, from Eq. 5, when \(r=1\), we have that \(A_{1}=A\setminus B_{0}^{1}=A\setminus \varnothing = A\).
- 7.
Furthermore, the problem of redundancy in \(\mathbb {O}(A_r)\) does not affect only the best mask \(B^{1}_{r}\). It is important to remark that it is also present for masks different from the best one. Therefore, it can be said that when the system is large, in each \(\mathbb {O}(A_r)\) a lack of variety comes up.
- 8.
The allocation in one exclusive cluster does not concern agents. The same agent can be detected in two masks that are not included in the same cluster.
- 9.
A soft partition is intended to be a set of masks of agents that do not necessarily belong to exclusively one masks. Therefore, as explained above, an agent can belong to more than one mask.
- 10.
From the first round \(r=1\), to the last round \(r=R\).
- 11.
The set \(\mathscr {P}_{R,v_{OV}}\) can present redundancies since, even if the rest of the system that at each new round r is analyzed does not include the best masks detected in round \((r - 1)\), it can include the agents that belong to the second/third/etc. masks detected in the round \((r - 1)\). Therefore, it could happen that those masks that were detected as second/third/etc. masks in \((r - 1)\), are detected also in the round r.
- 12.
While in Step 2 of the proposed methodology the SMC is used to evaluate similarity (see Sect. 5), in this Step the JC is considered as more appropriate. JC focuses its attention on the intersection of two masks (with regard of the union set), while SMC considers as a condition of similarity also the simultaneous absence of a same element. While in Step 2 was important to consider also the co-absence of agents as an element of similarity, so as to evaluate where the algorithm had moved (in terms of agents considered and not considered), here only the presence of overlapping agents, i.e. the intersection, is relevant.
- 13.
In this case study, the agents’ activities coincide with interactions. Agents are considered to be active when they are participating in a project. And since in each project partnerships have to be established (no single-participant projects are allowed), it follows that to be active implies to be interacting.
- 14.
Considering all the dates of starting and the ending of the projects, 59 different dates were identified.
- 15.
These variables assume four different values that correspond to one of the following four situations: inactivity, decreasing activity, stable activity or increasing activity. The ‘activity’ status is defined by considering the number of projects in which the agent is participating in the corresponding instant, with regard to the number of projects in which it was participating in the previous instant. With these series of variables, a second order Markov condition in taken into account, since agents’ activity is not described just for what is in each instant, but for what it is in the present conditioned to what it was in its nearest past. As a variation in time is considered, the number of variables finally computed equals the number of variables initially present minus 1.
- 16.
To have more than the 50% of agents producing an overlaps among the masks of a generic \(\mathbb {P}_{r,v_{OV}}\), or to allow in \(\mathscr {F}_{R,v_{OV},v_{SM}}\) couples of masks generating an intersection that is the 50% or more of the corresponding union set, has been considered as not pertinent for the objective of this work.
- 17.
Overlaps among groups (determined by the fact that each agent can belong in more than one group) are allowed and are present.
- 18.
In case of agents belonging together to more than one community, the corresponding \(t_{CI}\) have been summed.
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Righi, R., Samoili, S. (2018). Functional Interactions in Complex Networks: A Three-Step Methodology for the Implementation of the Relevance Index (RI). In: Pelillo, M., Poli, I., Roli, A., Serra, R., Slanzi, D., Villani, M. (eds) Artificial Life and Evolutionary Computation. WIVACE 2017. Communications in Computer and Information Science, vol 830. Springer, Cham. https://doi.org/10.1007/978-3-319-78658-2_16
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