- **A social interaction is a dynamic influence dissemination among persons through conversation, meeting, collective action etc. Communication is of particular interest since it**
often takes place on the electronic media, which is one of the major targets of surveillance.

- **An organization can be modeled as a social network which underlies below the social**
interaction. Nodes are persons. Links are relationship such as friendship, business partnership, chain of command etc. The links can be undirectional, unidirectional, or bidirectional. Variety of network topologies are known. A scale-free network[3] **and a small-world**
network[19] **were studied mathematically in detail. The topology of the real networks are**
diverse. The topologies of contemporary inter-working terrorists, self-organizing on-line community, and purposefully organized business team do not resemble.

- **The empty spot in the social interaction is the main topic of this contribution. It refers**
to an empty hard-to-fill space, which can exist in the observed records of the social interaction, and is the potential clue to the persons in the underlying social network who do not appear in the records. Such hidden persons are the origin of **the empty spot in a** nutshell.
In this contribution, the problem we address is to discover relevant **empty spots in a complex**
social interaction. We propose a heuristic predictor function method **to predict the relevant**
empty spots and the hidden persons from communication records. **The method is presented** in detail in 4 after studying the related works in 2 and the network models (homogeneous and inhomogeneous network) in 3. Simulation experiment is demonstrated in 5. A test data set is generated in the form of market baskets as the simulated communication records over a homogeneous network. Precision to discover the empty spots is calculated to evaluate the performance of the method for three trial cases. Concluding remarks are presented in 6.

## 2 Related Work

The problem is related to a node discovery problem[14],[16]**. Expertise in computer and social**
sciences is significant. Complex networks such as scale-free networks (Barab´asi-Albert model[3]) and small-world networks (Watts-Strogatz model[19]**) presented us insight on the structure and**
evolution of a large-scale network. Scientists' collaboration or actors in movies are examples.

Power law governing the scale-free network appears from the preferential attachment of the nodes in a growing network. A few very big hub nodes emerge, accounting for the winnertakes-all phenomena. The small-world network is highly clustered like **a regular lattice, but**
has small diameter like a random graph. The name originates in the small-world phenomena known as six degree of separation.

Search efficiency in a network[1] **is of particular interest for practical applications. The hub**
nodes in scale-free networks are useful in designing local search strategies. The hub nodes improve the efficiency to access relevant nodes. Error and attack tolerance were studied[2].

Scale-free networks display a surprisingly high degree of tolerance **against random errors. Other** networks do not have such a property. The error tolerance is, however, at the expense of attack survivability. The network is broken into many isolated fragments when the hub nodes are targeted. Centrality and brokerage measures[4],[5] **are convenient values summarizing the**
network topology. Degree, betweenness, closeness, and eigenvector centrality are popular among them. They have been studied in many cases of the social network analysis.

Empirical study on social networks uncovered many aspects of the criminal and terrorist organizations in the past and at present[17]. Intelligence sharing, knowledge management, and