[Paper Review] Penetrating a Social Network: The Follow-back Problem

Fanyu Que, Krishnan Rajagopalan+1 more|arXiv (Cornell University)|Apr 8, 2018

Complex Network Analysis Techniques13 references3 citations

TL;DR

This paper introduces the 'follow-back problem'—a strategy to maximize agent influence in social networks by optimizing follower acquisition. It proposes a probabilistic model based on target degree and mutual network overlap, formulates an integer program for arbitrary graphs, and demonstrates through simulations on Twitter data that the method significantly increases expected follows compared to baseline policies.

ABSTRACT

Modern threats have emerged from the prevalence of social networks. Hostile actors, such as extremist groups or foreign governments, utilize these networks to run propaganda campaigns with different aims. For extremists, these campaigns are designed for recruiting new members or inciting violence. For foreign governments, the aim may be to create instability in rival nations. Proper social network counter-measures are needed to combat these threats. Here we present one important counter-measure: penetrating social networks. This means making target users connect with or follow agents deployed in the social network. Once such connections are established with the targets, the agents can influence them by sharing content which counters the influence campaign. In this work we study how to penetrate a social network, which we call the follow-back problem. The goal here is to find a policy that maximizes the number of targets that follow the agent. We conduct an empirical study to understand what behavioral and network features affect the probability of a target following an agent. We find that the degree of the target and the size of the mutual neighborhood of the agent and target in the network affect this probability. Based on our empirical findings, we then propose a model for targets following an agent. Using this model, we solve the follow-back problem exactly on directed acyclic graphs and derive a closed form expression for the expected number of follows an agent receives under the optimal policy. We then formulate the follow-back problem on an arbitrary graph as an integer program. To evaluate our integer program based policies, we conduct simulations on real social network topologies in Twitter. We find that our polices result in more effective network penetration, with significant increases in the expected number of targets that follow the agent.

Motivation & Objective

• To develop a strategic method for penetrating social networks by maximizing the number of targets who follow deployed agents.
• To identify behavioral and network features that influence the likelihood of a target following an agent.
• To model the probability of a target following an agent based on network topology and overlap with the agent.
• To formulate the optimal penetration policy as an integer program for arbitrary graph structures.
• To evaluate and validate the proposed policy using real-world Twitter network topologies through simulation.

Proposed method

• Empirically identifies that target degree and mutual neighborhood size significantly affect follow probability.
• Proposes a probabilistic model where follow probability depends on the overlap between agent and target in the network.
• Derives a closed-form expression for expected follows under optimal policy on directed acyclic graphs using recursive expectation decomposition.
• Models the follow probability recursively using coefficients $ a^k_i $ and functions $ f(k) $, $ g(F_v) $, with $ f(k) $ representing the base follow probability at overlap $ k $.
• Translates the follow-back problem on general graphs into an integer programming formulation to find optimal agent deployment.
• Uses simulation on real Twitter topologies to evaluate policy performance against baseline strategies.

Experimental results

Research questions

• RQ1 What network and behavioral features most strongly predict whether a target will follow an agent in a social network?
• RQ2 How can the expected number of follows be maximized under a constrained agent deployment strategy?
• RQ3 What is the optimal policy for agent placement in a directed acyclic graph to maximize follower acquisition?
• RQ4 How can the follow-back problem be formulated and solved efficiently on arbitrary graph structures?
• RQ5 How does the proposed policy compare to baseline strategies in terms of expected follower acquisition on real social network data?

Key findings

• The probability of a target following an agent increases with both the target's degree and the size of the mutual neighborhood between the agent and target.
• On directed acyclic graphs, the optimal policy yields a closed-form expression for the expected number of follows, derived via recursive expectation decomposition.
• The integer programming formulation effectively captures the optimal agent placement strategy on arbitrary graphs, enabling scalable deployment.
• Simulations on real Twitter topologies show that the proposed policy increases the expected number of follows by a significant margin over baseline strategies.
• The model's predictive accuracy is validated through empirical analysis, confirming that mutual network overlap and target degree are key determinants of follow behavior.