What is the meaning of "valence" in this sentence?

From a New York times article about a summer program for poor students:

The valence among Vinay, Arshdeep and MD, and the 80 or so other mentors and their mentees forms the backbone of a new summer program called Practice Makes Perfect.

(source: http://opinionator.blogs.nytimes.com/2013/08/07/mentoring-students-to-prevent-the-summer-slide/?hp&_r=0)

According to the Merriam Webster online dictionary, the (most relevant) definition of valence is

the degree of attractiveness an individual, activity, or thing possesses as a behavioral goal

I don't see how that fits with how it's used in this sentence. What does valence mean here?

Valence

the capacity of one person or thing to react with or affect another in some special way, as by attraction or the facilitation of a function or activity.

Which is related to

Valence

In chemistry, valence, also known as valency or valence number, is the number of valence bonds a given atom has formed, or can form, with one or more other atoms

I believe he is talking about the special connections between the mentioned people

Although it is a strange choice by the author, I believe that the intended meaning of valence in this context is the one used in chemistry.

Carbon atoms are said to have a valence number (or valency) of +4 which enables each one to form up to four bonds to other atoms. When multiple carbon atoms are combined, long chains and complex rings can be formed that resemble the skeleton of a creature (or, in more modern terms, of a machine or building).

Organic chemists often refer to the carbon chain backbone upon which large molecules are built. By analogy the capacity of the named individuals to form multiple interconnections among themselves and to others provides the structural basis for the program being discussed.

Cognitive Valence Theory (CVT) is a theoretical framework for exploring the give and take of intimacy between two people. As the Wikipedia article on CVT suggests, physics provides CV theorists with an analogy based on the notions of negativity and positivity, attraction and repulsion. Intimacy in dyadic human relationships occurs in a number of different ways, both verbally and nonverbally, but the nonverbal aspects far outweigh the verbal in their sheer emotional valence. Probably 90 percent or more of the affective content of communication occurs nonverbally, with the verbal aspects contributing 10 percent or less.

The author of the NYT article you quote may or may not be thinking within a CVT framework, but I wouldn't fault him or her for not citing the theory. I imagine that among the 83 people in the Practice Makes Perfect program, there is a great deal of one-on-one (i.e., dyadic) interaction between mentors and mentees, and that intimacy (of a non-sexual nature, of course) is an important aspect of what the program is attempting to accomplish.

When mentors and mentees really open up to one another, and are at least somewhat transparent with and accountable to each other, defenses tend to come down and meaningful learning can take place. In that regard, one of my favorite sayings in the art of pedagogy is "More is caught than taught," which underscores the importance of a mentor's modeling of learning behaviors and imparting not only knowledge in general to the tutee but also the tools to encourage the tutee's lifelong learning.

If you can remember vividly a teacher, professor, or mentor who made a noticeably positive and constructive difference in your life, you probably connected with that person intellectually and emotionally.

Valence means

agglutination..

it shows one type of bonding between them to work together.. or in other words you can say

grouping, syndication, aggregation