Cognitive Profiling of Nodes in 6G through Multiplex Social Network and Evolutionary Collective Dynamics
<p>Multiplex representation mined from 6G subsystems. This figure shows the schematic representation through the multiplex network of a 6G scenario, including different types of sub-networks, various interactions and the evolutionary dynamics of collective phenomena.</p> "> Figure 2
<p>Modeling Approach: a technical scheme of nodes’ profiling in a 6G network scenario. The figure graphically describes the various steps and the key aspects to profile the elements that constitute the 6G scenario into a complex network heterogeneous environment of cognitive elements. The approach starts from the application of the complexity and the multiplex representation and analysis to extract structural features as detailed, respectively, in (<b>a</b>,<b>b</b>). The scheme shows the collective profiling based on the analysis of diffusion and competition, representing two co-evolving and interdependent dynamics, as, respectively, detailed in (<b>c</b>,<b>d</b>). The community profiling, as in (<b>e</b>,<b>f</b>), is characterized by the detection of communities based on node and link hierarchical clustering obtained through a multilink graph.</p> "> Figure 3
<p>Multiplex Network Representation. The figure describes both layers of the multiplex network <span class="html-italic">M</span>. The layer <math display="inline"><semantics> <msub> <mi>l</mi> <mn>1</mn> </msub> </semantics></math> is obtained from a real contact case, as explained in <a href="#sec3dot2-futureinternet-13-00135" class="html-sec">Section 3.2</a>, while the layer <math display="inline"><semantics> <msub> <mi>l</mi> <mn>2</mn> </msub> </semantics></math>, follows a theoretical scheme. Here, <math display="inline"><semantics> <msub> <mi>l</mi> <mn>2</mn> </msub> </semantics></math> is represented as a scale-free network. We shed light on the strength of each node (as the nodes’ size), and the awareness of each node (as the nodes’ color).</p> "> Figure 4
<p>Density of Involved Nodes <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">i</mi> <mo>(</mo> <mi mathvariant="bold-italic">t</mi> <mo>)</mo> </mrow> </semantics></math> versus time <math display="inline"><semantics> <mi mathvariant="bold-italic">t</mi> </semantics></math>, on the two processes in co-evolution. The outbreak of spreading in time is subjected to statistical variability. After a common exponential growth, we shed light on how the density of involved (“involved” means informed or infected) nodes <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">i</mi> <mo>(</mo> <mi mathvariant="bold-italic">t</mi> <mo>)</mo> </mrow> </semantics></math> change in two different cases (respectively, orange and red) of the co-evolving processes that can converge to zero (<math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">S</mi> <mi mathvariant="bold-italic">h</mi> </msub> <mi mathvariant="bold-italic">IR</mi> <mo>−</mo> <msub> <mi mathvariant="bold-italic">U</mi> <mi mathvariant="bold-italic">h</mi> </msub> <mi mathvariant="bold-italic">AF</mi> </mrow> </semantics></math>) or to a constant number (<math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">S</mi> <mi mathvariant="bold-italic">h</mi> </msub> <mi mathvariant="bold-italic">IS</mi> <mo>−</mo> <msub> <mi mathvariant="bold-italic">U</mi> <mi mathvariant="bold-italic">h</mi> </msub> <mi mathvariant="bold-italic">AU</mi> </mrow> </semantics></math>).</p> "> Figure 5
<p>Roles of Nodes from Structural Analysis. We show four panels to shed light on the roles of each node in <span class="html-italic">M</span> as a result of the structural profiling. At the top, the two heat-maps show with a color-code the value of degree <math display="inline"><semantics> <msubsup> <mi>k</mi> <mrow> <mi>i</mi> </mrow> <mi>α</mi> </msubsup> </semantics></math>, strength <math display="inline"><semantics> <msubsup> <mi>s</mi> <mrow> <mi>i</mi> </mrow> <mi>α</mi> </msubsup> </semantics></math> and overlapping degree <math display="inline"><semantics> <msub> <mi>o</mi> <mi>i</mi> </msub> </semantics></math> for each node, from the largest (darkest) to the smallest (brightest) in both cases of scale-free (SF) and small-world networks (SW) as assumption for the graph of the second layer of the multiplex that describes a social-based interaction graph, jointly with the first layer based on a real contact network (RC). Below, the other two panels show two cartography obtained by plotting, for each node, the multiplex participation coefficient <math display="inline"><semantics> <msub> <mi>P</mi> <mi>i</mi> </msub> </semantics></math> versus the Z-score of the total overlapping degree <math display="inline"><semantics> <msub> <mi>o</mi> <mi>i</mi> </msub> </semantics></math> in the cases of a theoretical distribution with high standard deviation <math display="inline"><semantics> <mi>δ</mi> </semantics></math> for low homophily and low standard deviation <math display="inline"><semantics> <mi>δ</mi> </semantics></math> for high homophily, referring to the distribution of similarity features among nodes. In both plots, comparing the cases <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>C</mi> <mo>−</mo> <mi>S</mi> <mi>F</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>C</mi> <mo>−</mo> <mi>S</mi> <mi>W</mi> </mrow> </semantics></math>, we identify specific roles of nodes put in evidence by the plots, in terms of focused, mixed, multiplex, regular or hubs nodes.</p> "> Figure 6
<p>Roles of Nodes from Collective Dynamics Analysis. We show four plots to shed light on the roles of each node of the population considered for the multiplex network <span class="html-italic">M</span> as a result of the collective profiling. The plots display, in the plane <math display="inline"><semantics> <mi>λ</mi> </semantics></math>-<math display="inline"><semantics> <mi>β</mi> </semantics></math>, the trend of involved rate in function of the awareness rate, comparing both cases of scale-free (SF) and small-world (SW) networks as assumption for the graph of the second layer of the multiplex that describe a social-based interaction graph, jointly with the first layer based on a real contact network (RC), showing in red color the <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>C</mi> <mo>−</mo> <mi>S</mi> <mi>F</mi> </mrow> </semantics></math> case, while in yellow the <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>C</mi> <mo>−</mo> <mi>S</mi> <mi>W</mi> </mrow> </semantics></math> case. In accordance with the model and the interdependence between the evolutionary dynamics linked to the co-evolving spreading processes and the evolutionary game theory, we set and compare the four social dilemmas (PD-SD-HG-SH) displaying the trend of the spreading dynamics in relation to the number of cooperation <math display="inline"><semantics> <msub> <mi>n</mi> <mi>c</mi> </msub> </semantics></math> for each node (as dot size variation) of the multiplex network <span class="html-italic">M</span>.</p> "> Figure 7
<p>Roles of Nodes from Community Analysis. In the (<b>a</b>,<b>b</b>) panel, we display the findings of the hierarchical clustering of nodes based on the score function <math display="inline"><semantics> <mrow> <mi>h</mi> <msub> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mrow> <mo>|</mo> </mrow> <mover accent="true"> <mi>G</mi> <mo>^</mo> </mover> </mrow> </msub> </mrow> </semantics></math>. In (<b>a</b>), we show the cluster dendrogram, with each colored square shedding lights on different node communities, determined by cutting the dendrogram at a specific height. In panel (<b>b</b>), we display the visualization of nodes communities using graph highlighting the six communities of the weighted aggregated graphs <math display="inline"><semantics> <mover accent="true"> <mi>G</mi> <mo>^</mo> </mover> </semantics></math>, whose interaction are referred to existing multilinks between a pair of nodes, and it is extracted from the multiplex network <span class="html-italic">M</span>. Moreover, we underline the multidegree values <math display="inline"><semantics> <msubsup> <mi>k</mi> <mi>i</mi> <mover accent="true"> <mi>m</mi> <mo>→</mo> </mover> </msubsup> </semantics></math> for each node in accordance with their size. In the panel (<b>c</b>,<b>d</b>), we exhibit the findings of a link-based clustering of the graph <math display="inline"><semantics> <mover accent="true"> <mi>G</mi> <mo>^</mo> </mover> </semantics></math> of the multiplex <span class="html-italic">M</span>, to detect the links communities. In (<b>c</b>), we show the cluster dendrogram highlighting the sixteen clusters detected. In (<b>d</b>), we illustrate the visualization of links communities using graph. Panel (<b>d</b>) shows a Spencer circle layout with numbers around the circumference of the circle that are referred to community ID.</p> ">
Abstract
:1. Introduction
2. Materials and Methods
2.1. Multiplex Social Network and Mesoscale Structure
2.2. Collective Dynamics of Diffusion and Competition
3. Results
3.1. Scenario
3.2. Structural Profiling
3.3. Collective Profiling
3.4. Community Profiling
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Structural Profiling | Formalism | Description |
---|---|---|
Parameters [9,13] | N | Population of Nodes of the Multiplex M |
M | Numbers of Layers of the Multiplex M | |
Adjacency Matrix of the Layer l | ||
Elements of the Matrix | ||
Degree of Node i in the Layer l | ||
Overlapping Degree of Node i | ||
Weighted Adjacency Matrix of the layer l | ||
Weighted Overlap of edge | ||
Weighted Overlapping Degree of node i | ||
Strength of node i in the layer l | ||
Inverse participation ratio of node i in the layer l | ||
Participation Coefficient of the node i | ||
Entropy of a node i | ||
Defined Metrics | Weights of interactions between | |
Homophily of a pair of nodes | ||
Awareness of a node i | ||
Attention of a node i during T around e |
Collective Profiling | Formalism | Description |
---|---|---|
Parameters [5] | Heterogeneous Susceptible State | |
I | Involved State | |
R | Recovered State | |
Heterogeneous Unaware State | ||
A | Aware State | |
F | Faded State | |
Probability to transit from state I to state R | ||
Fading Rate | ||
Density of Infected Node | ||
Defined Metrics | Heterogeneous involvement rate | |
Heterogeneous awareness rate | ||
Fermi function | ||
Impact factor of the co-evolving processes |
Community Profiling | Formalism | Description |
---|---|---|
Parameters [9,13] | Multilink between | |
Weighted Aggregated Network | ||
Elements of | ||
Multidegree of node i | ||
Number of cooperations | ||
Between-ness Centrality | ||
Defined Metrics | Score Function for dissimilarity structure |
Short Biography of Authors
| Marialisa Scatá received her B.S. (2005) and M.S. degrees (2009) in Telecommunication Engineering, from the Department of Electrical, Electronic and Computer Engineering (DIEEI), University of Catania, Italy. She received the Ph.D. in Computer Science and Telecommunication Engineering from University of Catania, in 2012, under the supervision of Prof. Aurelio La Corte, with whom she has been collaborating since 2009. Currently, she works as Postdoctoral Researcher at DIEEI, University of Catania. She serves as reviewer for several top-tier journals. She has an interdisciplinary approach to research and her interests include bio-inspired models, ICT, telecommunications, social networks, complex networks, multi-layer networks, social contagion and epidemic spreading, evolutionary game theory, data mining, machine learning, healthcare applications and cognitive networks. |
| Barbara Attanasio received her B.S. degree in Computer engineering (2016) and M.S. degree in Telecommunications engineering (2018) from the Dipartimento di Ingegneria Elettrica, Elettronica e Informatica (DIEEI) at University of Catania, Italy. She is currently a Ph.D. student in Systems, Energy, Computer and Telecommunications Engineering at DIEEI, University of Catania. Her research interests Multi Access Edge Computing, Evolutionary Game Theory, Multi-layer networks, Data Science and IoT. |
| Aurelio La Corte is Associate Professor in Telecommunication Engineering at the University of Catania, Italy. He received the degree in electrical engineering in 1988, and the Ph.D. in Electronic Engineering and Computer Science in 1994. He has more than 25 years of experience in scientific and teaching activity and specific experience in designing telecommunications networks and systems and in managing complex projects. Responsible for various ICT-related activities at the University of Catania, he has been involved in coordinating, designing and developing networks and ICT services.His scientific interests include telecommunication systems and integrated services, innovative ICT services and technological innovation. |
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Scatá, M.; Attanasio, B.; La Corte, A. Cognitive Profiling of Nodes in 6G through Multiplex Social Network and Evolutionary Collective Dynamics. Future Internet 2021, 13, 135. https://doi.org/10.3390/fi13050135
Scatá M, Attanasio B, La Corte A. Cognitive Profiling of Nodes in 6G through Multiplex Social Network and Evolutionary Collective Dynamics. Future Internet. 2021; 13(5):135. https://doi.org/10.3390/fi13050135
Chicago/Turabian StyleScatá, Marialisa, Barbara Attanasio, and Aurelio La Corte. 2021. "Cognitive Profiling of Nodes in 6G through Multiplex Social Network and Evolutionary Collective Dynamics" Future Internet 13, no. 5: 135. https://doi.org/10.3390/fi13050135