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Using graph theory to analyze biological networks.

Pavlopoulos GA, Secrier M, Moschopoulos CN, Soldatos TG, Kossida S, Aerts J, Schneider R, Bagos PG - BioData Min (2011)

Bottom Line: The myriad components of a system and their interactions are best characterized as networks and they are mainly represented as graphs where thousands of nodes are connected with thousands of vertices.In this article we demonstrate approaches, models and methods from the graph theory universe and we discuss ways in which they can be used to reveal hidden properties and features of a network.This network profiling combined with knowledge extraction will help us to better understand the biological significance of the system.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Computer Science and Biomedical Informatics, University of Central Greece, Lamia, 35100, Greece. pavlopou@embl.de.

ABSTRACT
Understanding complex systems often requires a bottom-up analysis towards a systems biology approach. The need to investigate a system, not only as individual components but as a whole, emerges. This can be done by examining the elementary constituents individually and then how these are connected. The myriad components of a system and their interactions are best characterized as networks and they are mainly represented as graphs where thousands of nodes are connected with thousands of vertices. In this article we demonstrate approaches, models and methods from the graph theory universe and we discuss ways in which they can be used to reveal hidden properties and features of a network. This network profiling combined with knowledge extraction will help us to better understand the biological significance of the system.

No MeSH data available.


Undirected, Directed, Weighted, Bipartite graphs. A. Undirected Graph: V = {V1, V2, V3, V4}, /V/ = 4, E = {(V1, V2), (V2, V3), (V2, V4), (V4, V1)}, /E/ = 4. B. Directed Graph: V = {V1, V2, V3, V4}, /V/ = 4, E = {(V1, V2), (V2, V3), (V2, V4), (V4, V1), (V4, V2)}, /E/ = 5. C. Weighted Graph: V = {V1, V2, V3, V4}, /V/ = 4, E = {(V1, V2, V4), (V2, V3, V2), (V2, V4, V9), (V4, V1, V8), (V4, V2, V6)}, /E/ = 5. D. Bipartite graph: V = {U1, U2, U3, U4, V1, V2, V3}, /V/ = 7, E = {(U1, V1), (U2, V1), (U2, V2), (U2, V3), (U3, V2), (U4, V2)}, /E/ = 6.
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Figure 1: Undirected, Directed, Weighted, Bipartite graphs. A. Undirected Graph: V = {V1, V2, V3, V4}, /V/ = 4, E = {(V1, V2), (V2, V3), (V2, V4), (V4, V1)}, /E/ = 4. B. Directed Graph: V = {V1, V2, V3, V4}, /V/ = 4, E = {(V1, V2), (V2, V3), (V2, V4), (V4, V1), (V4, V2)}, /E/ = 5. C. Weighted Graph: V = {V1, V2, V3, V4}, /V/ = 4, E = {(V1, V2, V4), (V2, V3, V2), (V2, V4, V9), (V4, V1, V8), (V4, V2, V6)}, /E/ = 5. D. Bipartite graph: V = {U1, U2, U3, U4, V1, V2, V3}, /V/ = 7, E = {(U1, V1), (U2, V1), (U2, V2), (U2, V3), (U3, V2), (U4, V2)}, /E/ = 6.

Mentions: Examples and shapes describing the aforementioned graph types can be found in Figure 1. The most common data structures that are used to make these networks computer readable are adjacency matrices or adjacency lists. The following section provides a short mathematical description of these data structures.


Using graph theory to analyze biological networks.

Pavlopoulos GA, Secrier M, Moschopoulos CN, Soldatos TG, Kossida S, Aerts J, Schneider R, Bagos PG - BioData Min (2011)

Undirected, Directed, Weighted, Bipartite graphs. A. Undirected Graph: V = {V1, V2, V3, V4}, /V/ = 4, E = {(V1, V2), (V2, V3), (V2, V4), (V4, V1)}, /E/ = 4. B. Directed Graph: V = {V1, V2, V3, V4}, /V/ = 4, E = {(V1, V2), (V2, V3), (V2, V4), (V4, V1), (V4, V2)}, /E/ = 5. C. Weighted Graph: V = {V1, V2, V3, V4}, /V/ = 4, E = {(V1, V2, V4), (V2, V3, V2), (V2, V4, V9), (V4, V1, V8), (V4, V2, V6)}, /E/ = 5. D. Bipartite graph: V = {U1, U2, U3, U4, V1, V2, V3}, /V/ = 7, E = {(U1, V1), (U2, V1), (U2, V2), (U2, V3), (U3, V2), (U4, V2)}, /E/ = 6.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3101653&req=5

Figure 1: Undirected, Directed, Weighted, Bipartite graphs. A. Undirected Graph: V = {V1, V2, V3, V4}, /V/ = 4, E = {(V1, V2), (V2, V3), (V2, V4), (V4, V1)}, /E/ = 4. B. Directed Graph: V = {V1, V2, V3, V4}, /V/ = 4, E = {(V1, V2), (V2, V3), (V2, V4), (V4, V1), (V4, V2)}, /E/ = 5. C. Weighted Graph: V = {V1, V2, V3, V4}, /V/ = 4, E = {(V1, V2, V4), (V2, V3, V2), (V2, V4, V9), (V4, V1, V8), (V4, V2, V6)}, /E/ = 5. D. Bipartite graph: V = {U1, U2, U3, U4, V1, V2, V3}, /V/ = 7, E = {(U1, V1), (U2, V1), (U2, V2), (U2, V3), (U3, V2), (U4, V2)}, /E/ = 6.
Mentions: Examples and shapes describing the aforementioned graph types can be found in Figure 1. The most common data structures that are used to make these networks computer readable are adjacency matrices or adjacency lists. The following section provides a short mathematical description of these data structures.

Bottom Line: The myriad components of a system and their interactions are best characterized as networks and they are mainly represented as graphs where thousands of nodes are connected with thousands of vertices.In this article we demonstrate approaches, models and methods from the graph theory universe and we discuss ways in which they can be used to reveal hidden properties and features of a network.This network profiling combined with knowledge extraction will help us to better understand the biological significance of the system.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Computer Science and Biomedical Informatics, University of Central Greece, Lamia, 35100, Greece. pavlopou@embl.de.

ABSTRACT
Understanding complex systems often requires a bottom-up analysis towards a systems biology approach. The need to investigate a system, not only as individual components but as a whole, emerges. This can be done by examining the elementary constituents individually and then how these are connected. The myriad components of a system and their interactions are best characterized as networks and they are mainly represented as graphs where thousands of nodes are connected with thousands of vertices. In this article we demonstrate approaches, models and methods from the graph theory universe and we discuss ways in which they can be used to reveal hidden properties and features of a network. This network profiling combined with knowledge extraction will help us to better understand the biological significance of the system.

No MeSH data available.