Limits...
Network morphospace.

Avena-Koenigsberger A, Goñi J, Solé R, Sporns O - J R Soc Interface (2015)

Bottom Line: The second is network science, which provides numerous quantitative tools to measure and classify different patterns of local and global network architecture across disparate types of systems.Defined by axes that represent specific network traits, each point within such a space represents a location occupied by networks that share a set of common 'morphological' characteristics related to aspects of their connectivity.Mapping a network morphospace reveals the extent to which the space is filled by existing networks, thus allowing a distinction between actual and impossible designs and highlighting the generative potential of rules and constraints that pervade the evolution of complex systems.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405-7007, USA.

ABSTRACT
The structure of complex networks has attracted much attention in recent years. It has been noted that many real-world examples of networked systems share a set of common architectural features. This raises important questions about their origin, for example whether such network attributes reflect common design principles or constraints imposed by selectional forces that have shaped the evolution of network topology. Is it possible to place the many patterns and forms of complex networks into a common space that reveals their relations, and what are the main rules and driving forces that determine which positions in such a space are occupied by systems that have actually evolved? We suggest that these questions can be addressed by combining concepts from two currently relatively unconnected fields. One is theoretical morphology, which has conceptualized the relations between morphological traits defined by mathematical models of biological form. The second is network science, which provides numerous quantitative tools to measure and classify different patterns of local and global network architecture across disparate types of systems. Here, we explore a new theoretical concept that lies at the intersection between both fields, the 'network morphospace'. Defined by axes that represent specific network traits, each point within such a space represents a location occupied by networks that share a set of common 'morphological' characteristics related to aspects of their connectivity. Mapping a network morphospace reveals the extent to which the space is filled by existing networks, thus allowing a distinction between actual and impossible designs and highlighting the generative potential of rules and constraints that pervade the evolution of complex systems.

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Hierarchy morphospace. The axes of this three-dimensional morphospace are given by treeness (T), feed-forwardness (F) and orderability (O). Coordinates of 125 real-world networks are indicated with filled circles, coloured according to network type (TECH, electronic circuits; GRN, GRNs; ECO, food webs; LANG, world corpora; MET, metabolisms; NEU, neuronal); four clusters can be identified, according to network's location within the morphospace. Non-coloured spheres represent ensemble of random networks of various sizes and degree distributions. Reproduced with permission from reference [70].
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RSIF20140881F4: Hierarchy morphospace. The axes of this three-dimensional morphospace are given by treeness (T), feed-forwardness (F) and orderability (O). Coordinates of 125 real-world networks are indicated with filled circles, coloured according to network type (TECH, electronic circuits; GRN, GRNs; ECO, food webs; LANG, world corpora; MET, metabolisms; NEU, neuronal); four clusters can be identified, according to network's location within the morphospace. Non-coloured spheres represent ensemble of random networks of various sizes and degree distributions. Reproduced with permission from reference [70].

Mentions: A recent study [70] employed a morphospace approach to examine the hierarchical features of complex networks and understand the forces that shape hierarchical directed networks. To characterize and quantify network hierarchy, three measures were defined: (i) treeness, a measure of how pyramidal the structure is; (ii) feed-forwardness, a measure of the impact of cyclic modules on the structure of a network, based on their position within the pyramidal structure; (iii) orderability, a measure of how orderable the network is, based on the fraction of nodes that does not belong to a cycle. Within the three-dimensional morphospace defined by these measures, an ensemble of random networks with homogeneous and heterogeneous degree distributions and 125 real-world networks of natural and artificial systems were located (figure 4). Surprisingly, in spite that four clusters of real-world networks with particular hierarchical features are distinguishable, almost all networks were found to occupy the same region occupied by the random ensemble. Because random networks are not considered to be optimally designed towards any structural trait, it is assumed that no selection pressures have restricted their occupation within the morphospace. Thus, the fact that real-world networks and random networks are located within the same region suggests that hierarchical order may be a by-product of random fluctuations that possibly emerge from selection for other structural traits, such as cost minimization or robustness against node and/or connection failure.Figure 4.


Network morphospace.

Avena-Koenigsberger A, Goñi J, Solé R, Sporns O - J R Soc Interface (2015)

Hierarchy morphospace. The axes of this three-dimensional morphospace are given by treeness (T), feed-forwardness (F) and orderability (O). Coordinates of 125 real-world networks are indicated with filled circles, coloured according to network type (TECH, electronic circuits; GRN, GRNs; ECO, food webs; LANG, world corpora; MET, metabolisms; NEU, neuronal); four clusters can be identified, according to network's location within the morphospace. Non-coloured spheres represent ensemble of random networks of various sizes and degree distributions. Reproduced with permission from reference [70].
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4305402&req=5

RSIF20140881F4: Hierarchy morphospace. The axes of this three-dimensional morphospace are given by treeness (T), feed-forwardness (F) and orderability (O). Coordinates of 125 real-world networks are indicated with filled circles, coloured according to network type (TECH, electronic circuits; GRN, GRNs; ECO, food webs; LANG, world corpora; MET, metabolisms; NEU, neuronal); four clusters can be identified, according to network's location within the morphospace. Non-coloured spheres represent ensemble of random networks of various sizes and degree distributions. Reproduced with permission from reference [70].
Mentions: A recent study [70] employed a morphospace approach to examine the hierarchical features of complex networks and understand the forces that shape hierarchical directed networks. To characterize and quantify network hierarchy, three measures were defined: (i) treeness, a measure of how pyramidal the structure is; (ii) feed-forwardness, a measure of the impact of cyclic modules on the structure of a network, based on their position within the pyramidal structure; (iii) orderability, a measure of how orderable the network is, based on the fraction of nodes that does not belong to a cycle. Within the three-dimensional morphospace defined by these measures, an ensemble of random networks with homogeneous and heterogeneous degree distributions and 125 real-world networks of natural and artificial systems were located (figure 4). Surprisingly, in spite that four clusters of real-world networks with particular hierarchical features are distinguishable, almost all networks were found to occupy the same region occupied by the random ensemble. Because random networks are not considered to be optimally designed towards any structural trait, it is assumed that no selection pressures have restricted their occupation within the morphospace. Thus, the fact that real-world networks and random networks are located within the same region suggests that hierarchical order may be a by-product of random fluctuations that possibly emerge from selection for other structural traits, such as cost minimization or robustness against node and/or connection failure.Figure 4.

Bottom Line: The second is network science, which provides numerous quantitative tools to measure and classify different patterns of local and global network architecture across disparate types of systems.Defined by axes that represent specific network traits, each point within such a space represents a location occupied by networks that share a set of common 'morphological' characteristics related to aspects of their connectivity.Mapping a network morphospace reveals the extent to which the space is filled by existing networks, thus allowing a distinction between actual and impossible designs and highlighting the generative potential of rules and constraints that pervade the evolution of complex systems.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405-7007, USA.

ABSTRACT
The structure of complex networks has attracted much attention in recent years. It has been noted that many real-world examples of networked systems share a set of common architectural features. This raises important questions about their origin, for example whether such network attributes reflect common design principles or constraints imposed by selectional forces that have shaped the evolution of network topology. Is it possible to place the many patterns and forms of complex networks into a common space that reveals their relations, and what are the main rules and driving forces that determine which positions in such a space are occupied by systems that have actually evolved? We suggest that these questions can be addressed by combining concepts from two currently relatively unconnected fields. One is theoretical morphology, which has conceptualized the relations between morphological traits defined by mathematical models of biological form. The second is network science, which provides numerous quantitative tools to measure and classify different patterns of local and global network architecture across disparate types of systems. Here, we explore a new theoretical concept that lies at the intersection between both fields, the 'network morphospace'. Defined by axes that represent specific network traits, each point within such a space represents a location occupied by networks that share a set of common 'morphological' characteristics related to aspects of their connectivity. Mapping a network morphospace reveals the extent to which the space is filled by existing networks, thus allowing a distinction between actual and impossible designs and highlighting the generative potential of rules and constraints that pervade the evolution of complex systems.

Show MeSH
Related in: MedlinePlus