Fundamentals of Network Biology

WenJun Zhang

• Publisher: WSPC (EUROPE)
• Year: 2018
• eBook ISBN: 9781786345103
• Topic: Medicine
• Subtopic: Bioinformatics

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As the first comprehensive title on network biology, this book covers a wide range of subjects including scientific fundamentals (graphs, networks, etc) of network biology, construction and analysis of biological networks, methods for identifying crucial nodes in biological networks, link prediction, flow analysis, network dynamics, evolution, simulation and control, ecological networks, social networks, molecular and cellular networks, network pharmacology and network toxicology, big data analytics, and more.

Across 12 parts and 26 chapters, with Matlab codes provided for most models and algorithms, this self-contained title provides an in-depth and complete insight on network biology. It is a valuable read for high-level undergraduates and postgraduates in the areas of biology, ecology, environmental sciences, medical science, computational science, applied mathematics, and social science.

--> Contents:

• Mathematical Fundamentals:
  • Fundamentals of Graph Theory
  • Graph Algorithms
  • Fundamentals of Network Theory
  • Other Fundamentals
• Crucial Nodes/Subnetworks/Modules, Network Types, and Structural Comparison:
  • Identification of Crucial Nodes and Subnetworks/Modules
  • Detection of Network Types
  • Comparison of Network Structure
• Network Dynamics, Evolution, Simulation and Control:
  • Network Dynamics
  • Network Robustness and Sensitivity Analysis
  • Network Control
  • Network Evolution
  • Cellular Automata
  • Self-Organization
  • Agent-based Modeling
• Flow Analysis:
  • Flow/Flux Analysis
• Link and Node Prediction:
  • Link Prediction: Sampling-based Methods
  • Link Prediction: Structure- and Perturbation-based Methods
  • Link Prediction: Node-Similarity-based Methods
  • Node Prediction
• Network Construction:
  • Construction of Biological Networks
• Pharmacological and Toxicological Networks:
  • Network Pharmacology and Toxicology
• Ecological Networks:
  • Food Webs
• Microscopic Networks:
  • Molecular and Cellular Networks
• Social Networks:
  • Social Network Analysis
• Software:
  • Software for Network Analysis
• Big Data Analytics:
  • Big Data Analytics for Network Biology

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--> Readership: Advanced undergraduates and graduate students and researchers in biology, ecology, pharmacology, applied mathematics, computational science, etc. -->
Keywords:Network Biology;Network Analysis;Food Webs;Molecular Networks;Social Networks;Network Pharmacology;Link Prediction;Network Dynamics;Big Data Analytics;Software;Models;Algorithms;Nodes;LinksReview:0

Part 1

Mathematical Fundamentals

Chapter 1

Fundamentals of Graph Theory

Graph theory is one of the most important fundamental sciences of network biology. Graph theory is a mathematical science with a long history (Chan et al., 1982; Gross and Yellen, 2005; Zhang, 2012e). As early in 1736, Euler solved the well-known Königsberg Bridges Problem and published the first paper on graph theory. However, graph theory was widely known and began to develop rapidly until the late and mid-20th century.

1.1Definitions and Concepts

A graph is a space made of some vertices and edges that connect vertices. Figure 1 shows a graph with 9 vertices and 14 edges. In other words, a graph X is an ordered triplet (V(X), E(X), φ), or ordered pair (V(X), E(X), in which V(X) is the nonempty vertex set, with vertices as elements, E(X) is the set of edges, with edges as elements, and φ is the incidence function that associates each edge (e) of X and un-ordered vertices (u, v), where φ(e) = (u, v).

Two vertices associated with the same edge are called adjacent vertices. Two edges associated with the same vertex are called adjacent. Two edges associated with the same vertex are called adjacency edges. For example, the vertices v₁ and v₂ in Fig. 1 are adjacent; the edges e₆ and e₁₀ are adjacent, and they are adjacency edges.

The edge with the same terminal vertex is called loop, i.e., the edge is a loop, given φ(e) = (u, u). The edge with different initial and terminal vertices is called link. There is no loop in Fig. 1, and all edges in Fig. 1 are links.

Fig. 1 A graph with nine vertices and 14 edges (Zhang, 2012e).

The vertex without linking any edge is called isolated vertex.

The graph in Fig. 1 can be mathematically represented as follows:

or

The graph without any vertex and edge is a null graph, denoted by ϕ.

1.1.1Finite graph and infinite graph

A graph is a finite graph if it has a finite number of vertices (i.e., the vertex set V is a finite set) and a finite number of edges (i.e., the edge set E is a finite set). Figure 1 is a finite graph.

1.1.2Simple graph and planar graph

The edges e₁ and e₂ are called parallel edges, given φ(e₁) = φ(e₂). If a graph has neither loops nor parallel edges, it is called simple graph. Figure 1 is a simple graph. Figure 2(a) is not a simple graph. There is a loop (e₂) and two parallel edges (e₅, e₆) in Fig. 2(a).

In a graph X, delete all loops, so that every pair of adjacent edges have one link only, the resulting simple graph is the basic simple graph of graph X.

In a graph in which any two edges do not intersect each other but they intersect at the endpoints is called planar graph, or else it is a nonplanar graph. A planar graph can be drawn on a plane in a simple way. Figure 1 is a planar graph, and Fig. 2(b) is a nonplanar graph.

Fig. 2 Nonsimple graph (a) and nonplanar graph and (b) (Zhang, 2012e).

1.1.3Subgraph, proper subgraph, spanning subgraph, complementary graph

Given

and

and φ_Y is the restriction of φ_X on E(Y), Y is called the subgraph of X, denoted by

In this case, the vertex set and edge set of Y are subsets of the vertex set and edge set of X, respectively.

For example, in Fig. 1, the graph

is a subgraph of Fig. 1.

Given

and Y ≠ X, i.e., if the graph Y does not contain all edges of X, Y is called the proper subgraph of X. The Y above is the proper subgraph of Fig. 1.

Given V(Y) = V(X), i.e., if the subgraph Y contains all vertices of X, Y is the spanning subgraph of X. For example, remove the edges e₇ and e₈, the rest of the graph is a spanning subgraph of Fig. 1.

Suppose

and V′ is the vertex set, and the group of edges with two endpoints in V′, the ...

Table of contents

• Cover
• Halftitle
• Series Editors
• Title
• Copyright
• Preface
• About the Author
• Acknowledgments
• Contents
• Part 1 Mathematical Fundamentals
• Part 2 Crucial Nodes/Subnetworks/Modules, Network Types, and Structural Comparison
• Part 3 Network Dynamics, Evolution, Simulation, and Control
• Part 4 Flow Analysis
• Part 5 Link and Node Prediction
• Part 6 Network Construction
• Part 7 Pharmacological and Toxicological Networks
• Part 8 Ecological Networks
• Part 9 Microscopic Networks
• Part 10 Social Networks
• Part 11 Software
• Part 12 Big Data Analytics
• References
• Index