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Searchability of networks
Umeå University, Faculty of Science and Technology, Physics.
Umeå University, Faculty of Science and Technology, Physics.
Umeå University, Faculty of Science and Technology, Physics.
NORDITA, Blegdamsvej 17, Dk 2100, Copenhagen, Denmark.
2005 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 72, no 4, 046117-046125 p.Article in journal (Refereed) Published
Abstract [en]

We investigate the searchability of complex systems in terms of their interconnectedness. Associating searchability with the number and size of branch points along the paths between the nodes, we find that scale-free networks are relatively difficult to search, and thus that the abundance of scale-free networks in nature and society may reflect an attempt to protect local areas in a highly interconnected network from nonrelated communication. In fact, starting from a random node, real-world networks with higher order organization like modular or hierarchical structure are even more difficult to navigate than random scale-free networks. The searchability at the node level opens the possibility for a generalized hierarchy measure that captures both the hierarchy in the usual terms of trees as in military structures, and the intrinsic hierarchical nature of topological hierarchies for scale-free networks as in the Internet.

Place, publisher, year, edition, pages
American Physical Society , 2005. Vol. 72, no 4, 046117-046125 p.
Identifiers
URN: urn:nbn:se:umu:diva-5249DOI: 10.1103/PhysRevE.72.046117OAI: oai:DiVA.org:umu-5249DiVA: diva2:144702
Available from: 2006-08-31 Created: 2006-08-31 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Complex patterns: from physical to social interactions
Open this publication in new window or tab >>Complex patterns: from physical to social interactions
2006 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Interactions are what gives us the knowledge of the world around us. Interactions on all levels may fundamentally be seen as an exchange of information and a possible response of the same. Whether it is an electron in an electrical field or a handsome dude in a bar responding to a flirtation---interactions make things happen. In this sense we can see that objects without the capability of interacting with each other also are invisible to each other. Chains of pairwise interacting entities can serve as mediators of indirect interactions between objects. Nonetheless, in the limit of no interactions, we get into a philosophical debate whether we actually may consider anything to exist since it can not be detected in any way. Interactions between matter tend to be organized and show a hierarchical structure in which smaller sub-systems can be seen as parts of a bigger system, which in turn might be a smaller part of an even bigger system. This is reflected by the fact that we have sciences that successfully study specific interactions between objects or matter---physics, chemistry, biology, ecology, sociology,... What happens in a situation where all length scales are important? How does the structure of the underlying network of interactions affect the dynamical properties of a system? What network structures do we find and how are they created? This thesis is a physicist's view of collective dynamics, from superconductors to social systems and navigation in city street networks.

Place, publisher, year, edition, pages
Umeå: Fysik, 2006. 60 p.
Keyword
Complex networks, collective dynamics, statistical physics, random graphs
National Category
Other Physics Topics
Identifiers
urn:nbn:se:umu:diva-801 (URN)91-7264-090-1 (ISBN)
Public defence
2006-06-02, N430, Naturvetarhuset, Umeå Universitet, Umeå, 13:15 (English)
Opponent
Supervisors
Available from: 2006-05-12 Created: 2006-05-12 Last updated: 2011-04-26Bibliographically approved
2. Information horizons in a complex world
Open this publication in new window or tab >>Information horizons in a complex world
2006 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The whole in a complex system is the sum of its parts, plus the interactions between the parts. Understanding social, biological, and economic systems therefore often depends on understanding their patterns of interactions---their networks. In this thesis, the approach is to understand complex systems by making simple network models with nodes and links. It is first of all an attempt to investigate how the communication over the network affects the network structure and, vice versa, how the network structure affects the conditions for communication.

To explore the local mechanism behind network organization, we used simplified social systems and modeled the response to communication. Low communication levels resulted in random networks, whereas higher communication levels led to structured networks with most nodes having very few links and a few nodes having very many links. We also explored various models where nodes merge into bigger units, to reduce communication costs, and showed that these merging models give rise to the same kind of structured networks.

In addition to this modeling of communication networks, we developed new ways to measure and characterize real-world networks. For example, we found that they in general favor communication on short distance, two-three steps away in the network, within what we call the information horizon.

Abstract [sv]

Helheten i ett komplext system är mer än summan av dess delar, då den även inbegriper interaktionerna mellan dem. Att studera sociala, biologiska och ekonomiska system blir därför ofta en fråga om att förstå deras interaktionsmönster, d.v.s. deras nätverk av noder och länkar. Med utgångspunkt i enkla nätverksmodeller undersöker avhandlingen i huvudsak hur kommunikation i nätverk påverkar nätverksstrukturen och, vice versa, hur nätverksstrukturen påverkar villkoren för kommunikation.

Vi utforskade mekanismerna bakom hur nätverk är organiserade genom att modellera effekten av kommunikation i förenklade sociala system. En låg kommunikationsnivå visade sig ge upphov till kaotiska nätverk där ingen nod i princip hade fler länkar än någon annan. En hög kommunikationsnivå resulterade däremot i strukturerade nätverk, med några få centrala noder med många länkar, medan flertalet noder var perifera med enbart några få länkar. Det visade sig också att alla aktörer i nätverket gynnades av kommunikation, även när den var ojämnt fördelad. Kvaliteten på kommunikationen, d.v.s. informationens giltighet, var också avgörande för vilka positioner som gynnades i ett nätverk, vilket vi visade genom att studera aktörer som spred falsk information.

Eftersom effektiv kommunikation är en viktig del i många nätverk betraktar vi utvecklingen av dem som en optimeringsprocess. Varje kommunikationshandling mellan noderna tar tid och genom att slå sig samman till större enheter begränsas dessa kostnader och gör nätverket effektivare. Dessa s.k. sammanslagningsmodeller gav upphov till samma typ av strukturerade nätverk som ovan.

Genom att utveckla olika sätt att mäta nätverksstrukturer visade vi bland annat att många verkliga system främjar kommunikation över korta avstånd, två-tre steg bort i nätverket, innanför det vi kallar informationshorisonten. Vi uppskattade också den mängd information som krävs för att orientera sig i städer, och fann att det är lättare att hitta i moderna, planerade städer än i äldre städer som utvecklats under lång tid.

Place, publisher, year, edition, pages
Department of Physics, 2006. 76 p.
Keyword
Complex systems, networks, information, communication, self-organization, network topology, agent-based modeling.
National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-840 (URN)9172641177 (ISBN)
Public defence
2006-08-22, MA121, MIT-huset, Umeå universitet, Umeå, 13:00 (English)
Opponent
Supervisors
Available from: 2006-08-31 Created: 2006-08-31 Last updated: 2010-03-12Bibliographically approved

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