<figure><img src="image_1.png" /></figure>

HAL
open science

Complex Networks Dynamics

Cyrille Bertelle, M.A. Aziz-Alaoui

► To cite this version:

Cyrille Bertelle, M.A. Aziz-Alaoui. Complex Networks Dynamics. MATEC Web of Conferences, 2012, 1, pp.07002. 10.1051/matecconf/20120107002. hal-02123689

HAL Id: hal-02123689

https://hal.science/hal-02123689v1

Submitted on 22 May 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Complex Networks Dynamics

Cyrille Bertelle<fnref n="1" />,<fnref n="3" />,ª and M.A. Aziz-Alaoui<fnref n="2" />,<fnref n="3" />

**Abstract.** This paper proposes a conceptual approach to study conceptual links in complex systems between dynamics, structure and control. Studies cases are presented and are developed, using a java library on dynamical graphs called GraphStream.

# 1 Goals, Scientific Position and Approaches

One of the main characteristics of complexity is the emergence of properties, as synchronization, due to dynamical processes. Our objective is to contribute to the formalization of these emergent properties studying dynamical structures. The complexity dynamics is not only a one-way expression of the structure properties, but the structure itself controls the dynamics of the whole. The structures of complexity proposed here, are interaction systems as the core of self-organization mechanisms. During morphogenesis or more generally along morphodynamics, the structure topology is emergent or evolving [2]. Dynamical networks are efficient tools to express some local or global properties of this evolving topology. They capture structural aspects of complex systems representing entities as nodes and interactions between them as links. There are many experimental and analytical evidences that the network topology crucially influences essential network properties, such as resilience and tolerance to attacks, spreading processes, but also the collective dynamics phenomenon, such as self-organization and synchronization [1, 10].

Our purpose is to describe complex systems and their constitutive entities as the result of a process coming from the interaction of the three concepts: Structure, Dynamics and Control (see Figure 1). This triangular conceptual model can summerized our approach in modeling various phenomena:

- *Morphogenesis* is the result of dynamical flux on entities leading to an emergent structure under a self-organizational process making co-evolute entities, structures and dynamics.

- *Network synchronization* could be controlled by its topology. We are interesting on understanding how does the network structure impact on dynamics.

- *Topology identification* of network of interacting dynamical systems can be processed by an adaptive control.

We give in section 2, examples of this three-part interacting system of concepts characterizing the complexity

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Complex systems description based on the three-part interacting concepts: Structure, Dynamics and Control</figcaption></figure>

of the studied phenomena. In section 3, we describe the dynamical graph library, called GraphStream, allowing to manipulate dynamics of networks involved in the section 2.

# 2 Complex Network Dynamics: Applications

## 2.1 Network synchronization

Synchronization of networks, with nodes corresponding to dynamical systems, leads to relevent applications as in brain dynamics and neuroscience. Various synchrony behaviors can arise in such a case, among them, identical or burst synchronization produced by slow-fast dynamics [3]. The coupling strength of dynamical system for burst synchronization is sensitive to the network topology, like the average in-degree, described in the Figure 2.

## 2.2 Community Detection Algorithms on Dynamical Graphs

Community detection on dynamical graphs has practical applications for adaptive computing distribution of decentralized models. In Figure 3, we observe a swarm intelligence process based on a combinaison of cooperative-competitive colored ants colonies<fnref n="1" />, and making emerge a

<footnote n="1">¹ LITIS, University of Le Havre, 25 rue Ph. Lebon, B.P. 540, 76058 Le Havre cedex, France</footnote>

<footnote n="2">² LMAH, University of Le Havre, 25 rue Ph. Lebon, B.P. 540, 76058 Le Havre cedex, France</footnote>

<footnote n="3">³ ISCN, University of Le Havre, 25 rue Ph. Lebon, B.P. 540, 76058 Le Havre cedex, France</footnote>

<footnote>ª e-mail: cyrille.bertelle@univ-lehavre.fr</footnote>

<footnote n="1">¹ This original swarm intelligence algorithm on dynamical graph is called AntCO2</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Coupling strength to synchronize networks with different average in-degree</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Graph clustering with AntCO2</figcaption></figure>

dynamical clustering over a dynamical graph describing communications between entities of a program [4].

## 2.3 Urban Vulnerability Analysis based on Road Network Morphodynamics

Urban population protection during possible technological risks could lead to analyse the road network morphodynamics in order to measure vulnerability during a global evacuation process of a whole city. Figure 4 shows a dynamical process over road network of Le Havre city to detect morphodynamical properties, as element of vulnerability measures [8, 7, 6].

## 3 A Computing Ressource: GraphStream

The previous applications have been developed with Graph-Stream<fnref n="2" /> which is an open-source java library implemented by the RI2C team of the research laboratory LITIS [5]. The expression of dynamics is the major specificity of this library making simulations based on dynamical graphs. A dynamical graph is basically described by a stream of events, corresponding to additions or removals of nodes, edges or attributes on them. Figure 5 is a two-windows simulation where the left window is the output of an artificial

ecosystem where various animal species are crossing space with collective moves following boids algorithm [9]. The rigth window is a dynamical graph composed from the ecosystem simulation, extracting entities and creating the graph of communications between them. During the dynamical graph building a swarm intelligence process is running over it in order to detect communication clusters which are represented by colored nodes and edges. An automatic display is implemented in GraphStream allowing to aggregate high density connected region of dynamical graph. The two curves on the bottom of the right window give two indicators measuring clustering and load-balancing efficiencies.

## Acknowledgment

This paper is the result of various interactions with members of our research teams. The authors thank their close collaborators: Stefan Balev, Nathalie Corson, Antoine Dutot, Rawan Ghnemat, Frédéric Guinand, Michel Nabaa, Damien Olivier, Yoann Pigné and Guilhelm Savin. The authors would like also to thank The FEDER RISC<fnref n="3" /> and the Region Haute-Normandie for their numerous supports allowing to develop fondamental and applied research expressed in this paper.

## References

1. Barrat, A.; Barthélemy, M & Vespignani, A. *Dynamical Processes on Complex Networks*, (Cambridge University Press, 2008).

2. Bourgine, P. & Lesne, A. *Morphogenesis - Origin of Patterns and Shape*, (Springer, 2011).

3. Corson, N. & Aziz-Alaoui, M.A. “Complex emergent properties in synchronized neuronal oscillations”, From System Complexity to Emergent Properties, Springer, Understanding Complex Systems series, Eds. M.A. Aziz-Alaoui and Cyrille Bertelle, 2009, pp 243-259.

4. Dutot, A. *Distribution dynamique adaptative à lâaide de mécanismes dâintelligence collective*, Ph.D. thesis, 2005, University of Le Havre, France.

5. Dutot, A., Guinand, F., Olivier, D. & Pigné, Y., “Graph-Stream: A Tool for bridging the gap between Complex Systems and Dynamic Graphs”, *Proceedings: EPNACS: Emergent Properties in Natural and Artificial Complex Systems*, 2007, http://graphstream-project.org/

6. Nabaa, M. *Morphodynamique de réseaux viaires. Application au risque*, PhD in Computer Science, (University of Le Havre, 2011), 246 pages.

7. Nabaa, M., Bertelle, C., Olivier, D., Dutot, A., Mallet, P., *Communities detection algorithm to minimize risk during an evacuation* in proceedings of IEEE International Systems Conferenece, April 5-8, 2010, San Diego, California, USA.

8. Nabaa, M., Bertelle, C., Dutot, A., Olivier, D., Lions, P., *Exploitation of a displacement survey to detect road network use vulnerability*, in proceeding ICCSA 2009, June 29-July 02, 2009, University of Le Havre, pp 151-156.

<footnote n="3">³ RISC is a French Acronym for Complex Networks and Systems</footnote>

<footnote n="2">² http://graphstream-project.org</footnote>
<figure><img src="image_6.png" /><figcaption>Fig. 4. Morphodynamics of the Road Network of Le Havre City to Study the Urban Vulnerability</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 5. Adaptive distribution of a dynamical simulation with AntCo2 algorithm implemented in GraphStream Library</figcaption></figure>

9. Reynolds, C.W. "Flocks, herds, and schools: A distributed behavioral model", *Computer Graphics (SIGGRAPH '87 Conference Proceedings)*, 1987, **21 (4)**, 25-34.

10. Wu, C.W. *Synchronization in Complex Networks of Nonlinear Dynamical Systems*, (World Scientific Publishing, 2007).