[Paper Review] How to Build Your Network? A Structural Analysis

Anastasia Moskvina, Jiamou Liu|arXiv (Cornell University)|May 12, 2016

Complex Network Analysis Techniques19 references9 citations

TL;DR

This paper proposes an algorithmic framework for optimizing network building—specifically, how a newcomer can strategically form ties with an existing network to achieve structural advantages such as centrality or reduced diameter. It proves the centrality optimization problem is NP-complete but demonstrates that efficient heuristics require only a small number of new edges, even in large networks.

ABSTRACT

Creating new ties in a social network facilitates knowledge exchange and affects positional advantage. In this paper, we study the process, which we call network building, of establishing ties between two existing social networks in order to reach certain structural goals. We focus on the case when one of the two networks consists only of a single member and motivate this case from two perspectives. The first perspective is socialization: we ask how a newcomer can forge relationships with an existing network to place herself at the center. We prove that obtaining optimal solutions to this problem is NP-complete, and present several efficient algorithms to solve this problem and compare them with each other. The second perspective is network expansion: we investigate how a network may preserve or reduce its diameter through linking with a new node, hence ensuring small distance between its members. We give two algorithms for this problem. For both perspectives the experiment demonstrates that a small number of new links is usually sufficient to reach the respective goal.

Motivation & Objective

• To formalize and algorithmically study the process of network building, particularly when a newcomer joins an existing network.
• To address two key structural goals: placing the newcomer at the network center (socialization) and minimizing the network’s diameter (network expansion).
• To develop efficient algorithms that minimize the number of new ties while achieving desired structural properties.
• To empirically evaluate algorithm performance on synthetic and real-world networks, focusing on edge efficiency and scalability.

Proposed method

• Proposes two main problems: (1) minimizing new edges for a newcomer to achieve centrality (center problem), and (2) minimizing new edges to reduce or preserve network diameter (diameter improvement problem).
• Proves the center problem is NP-complete, establishing computational hardness of optimal solutions.
• Introduces heuristic algorithms: Periphery (iteratively connecting to peripheral node pairs) and CP (Center-Periphery, connecting to a central node and then peripheral nodes).
• Employs a simplification process to improve algorithmic performance by reducing redundant computations.
• Uses random graph models (Barabási-Albert and Newman-Watts-Strogatz) and real-world datasets (Collaboration, Facebook) for experimental validation.
• Measures performance via the number of new edges required to achieve target structural properties (e.g., diameter ≤ Δ).

Experimental results

Research questions

• RQ1 What is the computational complexity of placing a newcomer at the center of an existing network via minimal new ties?
• RQ2 How can a network be expanded with a new node while minimizing the number of new edges and preserving or reducing its diameter?
• RQ3 Which heuristic performs better under varying network topologies—especially in terms of edge efficiency?
• RQ4 How does the number of required new edges scale with network size for achieving structural goals?
• RQ5 Can a small number of strategic ties significantly improve key network properties like diameter or centrality in real-world networks?

Key findings

• The problem of placing a newcomer at the center of a network is NP-complete, confirming the computational difficulty of achieving optimal solutions.
• Despite NP-completeness, heuristic algorithms like Periphery and CP achieve the desired structural goals with very few new edges.
• On real-world collaboration networks, reducing the diameter by one requires fewer than 19 new edges, even for large networks.
• For the Facebook network, the Periphery algorithm required only 2 edges to reduce diameter from 8 to 7, while CP required 47, demonstrating significant performance differences.
• The Periphery algorithm outperforms CP when the network radius is close to its diameter, while CP performs better when the radius is much smaller than the diameter.
• The experiments reveal a robust phenomenon: even large networks can achieve significant structural improvements with minimal new ties, suggesting high efficiency of strategic network building.